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class complex
<h1><a name="oldcomplex">The Complex Class</a> </h1> This chapter describes: <ul> <li> How to use complex numbers with the class complex <li> Functions in the library: <ul> <li> Constructor function <li> Operator functions <li> Complex functions <li> Trigonometric and hyperbolic functions <li> Mathematical functions </ul> </ul> Class complex is implemented as a set of overloaded operators and functions that perform general complex mathematics. A complex number has two data members: a real and an imaginary part. Both are of type double. <p> This class implements complex numbers. Using overloaded functions and operators, you can treat complex numbers like you treat reals or integers. You can use the following: <ul> <li> Arithmetic operators (+, -, /, *), relational operators (==, !=), and logical operators (&&, ||)<br> <li> Stream operators << and >>.<br> <li> Mathematical functions, such as sqrt() and log10().<br><br> </ul> <h2>Using the Complex Class</h2> To use complex numbers, add the library complex to your project and include file oldcomplex.h in your file, in a statement like this: <pre>#include <oldcomplex.h> </pre> You can declare a complex variable three ways: uninitialized, initialized with two numbers, or initialized with another complex number. For example: <pre>complex z1; // Uninitialized complex z2(1.0,2.0); // Initialized with two numbers complex z3 = z2; // Initialized with a complex number </pre> To access components of a complex number, use member functions complex::real() and complex::imag(). For example: <pre>complex z1, z2(5.0,6.0); z1.real() = z2.imag(); z1.imag() = z2.real(); </pre> To print or read a complex number, use stream operators operator>> and operator<<. For example, this program: <pre>#include <complex.h> #include <iostream.h> int main() { complex z1(1.1, 2.0), z2; cout << "Enter z2: "; cin >> z2; cout << "z1 = " << z1 << '\n'; cout << "z2 = " << z2 << '\n'; return 0; } </pre> prints this: <pre>Enter z2: 10 9.8 z1 = (1.1, 2) z2 = (10,9.8) </pre> You can also use a complex number in the middle of a statement. For example, this line prints out the sine of (1, 1): <pre>cout << sin(complex(1,1)); </pre> <strong>Note:</strong> To invoke the complex version of a function, one of its arguments must be complex. For example, to figure the square root of -1, you must use sqrt(complex(-1,0)). <p> <h3>Member Functions</h3> The five types of class member functions are: <ul> <li> Constructors <li> Operators <li> Complex <li> Trigonometric and hyperbolic <li> Mathematical </ul> <hr><h3>Constructor Function</h3> The following function is a constructor function.<br><br> <hr> <h2><a name="complex::complex()">complex::complex()</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex::complex();<br> complex::complex(double re, double im);<br> complex::complex(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>The first constructor creates an unitialized complex number. For example: <pre>complex z; </pre> The second constructor creates a complex number with the real part initialized to re and the imaginary part initialized to im. For example: <pre>complex z1(1.2,3.0), z2(3,4); </pre> The third constructor creates a copy of a complex number. It is also called the X(X&) constructor. For example:<br><br> <pre>#include <oldcomplex.h> complex complexFunc() { // Invokes complex(double, double) complex z1(2.0,4.0); // Invokes complex(const complex&) complex z2 = z1; // Invokes complex(const complex&) to // create a temporary variable and adds // it to z1. return complex(1.1, 2.2) + z1; } </pre> </dd> </dl> <h3>Operator Functions</h3> The operators defined for complex are overloaded to have the same meaning as the built-in operators. For example, + is the addition of two complex variables just as it is used for the addition of two variables of type double. The operators in the complex class have the usual operator precedence.<br><br> The five types of operators defined for the complex class are: <br><br> <div class="naked_tr"> arithmetic operator+<br> operator-<br> operator*<br> operator/</div> <div class="naked_tr"> relational operator&&<br> operator||<br> operator!<br> operator==</div> <div class="naked_tr"> assignment complex::operator=<br> complex::operator+=<br> complex::operator-=<br> complex::operator*<br> complex::operator/</div> <div class="naked_tr"> unary complex::operator-<br> complex::operator!</div> <div class="naked_tr"> stream operator<<<br> operator>></div> <hr> <h2><a name="complex::operator=">complex::operator=</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex& complex::operator=(const complex& z);<br> complex& complex::operator=(double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Assigns a value to complex variable. </dd> </dl> <hr> <h2><a name="complex::operator+=">complex::operator+=</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex& complex::operator+=(const complex& z);<br> complex& complex::operator+=(double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Adds a value to a complex variable and assigns the result to the complex variable. </dd> </dl> <hr> <h2><a name="complex::operator-=">complex::operator-=</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex& complex::operator-=(const complex& z);<br> complex& complex::operator-=(double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Subtracts a value from a complex variable and assigns the result to the complex variable. </dd> </dl> <hr> <h2><a name="complex::operator*=">complex::operator*=</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex& complex::operator*=(const complex& z);<br> complex& complex::operator*=(double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Multiplies a value by a complex variable and assigns the result to the complex variable. </dd> </dl> <hr> <h2><a name="complex::operator/=">complex::operator/=</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex& complex::operator/=(const complex& z);<br> complex& complex::operator/=(double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Divides a complex variable by a value and assigns the result to the complex variable. </dd> </dl> <hr> <h2><a name="complex::operator-">complex::operator-</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex complex::operator-() const; </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the negative of a complex number. </dd> </dl> <hr> <h2><a name="complex::operator!">complex::operator!</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>int complex::operator!() const; </tt></dd> <dt><strong>Description</strong></dt> <dd>Performs logical negation on a complex number. </dd> </dl> <hr> <h2><a name="operator+">operator+</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex operator+(const complex& z1, complex& z2);<br> complex operator+(double u, const complex& z);<br> complex operator+(const complex& z, double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the sum of a complex number and any other number. </dd> </dl> <hr> <h2><a name="operator-">operator-</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex operator-(const complex& z1, const complex& z2);<br> complex operator-(double u, const complex& z);<br> complex operator-(const complex& z, double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the difference of a complex number and any other number. </dd> </dl> <hr> <h2><a name="operator*">operator*</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex operator*(const complex& z1, const complex& z2);<br> complex operator*(double u, const complex& z);<br> complex operator*(const complex& z, double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the product of a complex number and any other number. </dd> </dl> <hr> <h2><a name="operator/">operator/</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex operator/(const complex& z1, const complex& z2);<br> complex operator/(double u, const complex& z);<br> complex operator/(const complex& z, double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the quotient of a complex number and any other number. </dd> </dl> <hr> <h2><a name="operator&&">operator&&</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex operator&&(const complex& z1, const complex& z2);<br> complex operator&&(double u, const complex& z);<br> complex operator&&(const complex& z, double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Performs logical AND. Returns 0 if both arguments are 0 or (0, 0). </dd> </dl> <hr> <h2><a name="operator|| ">operator|| </a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex operator||(const complex& z1, const complex& z2);<br> complex operator||(double u, const complex& z);<br> complex operator||(const complex& z, double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Performs logical OR. Returns 0 if both arguments are 0 or (0, 0). </dd> </dl> <hr> <h2><a name="operator!">operator!</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex operator!=(const complex& z1, const complex& z2);<br> complex operator!=(double u, const complex& z);<br> complex operator!=(const complex& z, double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Tests for inequality. </dd> </dl> <hr> <h2><a name="operator==">operator==</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex ::operator==(const complex& z1, const complex& z2);<br> complex ::operator==(double u, const complex& z);<br> complex ::operator==(const complex& z, double u); </tt></dd> <dt><strong>Description</strong></dt> <dd>Tests for equality. </dd> </dl> <hr> <h2><a name="operator<<">operator<<</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>ostream& operator<<(ostream& s, const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>Reads z from the stream s, in the form(real, imaginary). </dd> </dl> <hr> <h2><a name="operator>>">operator>></a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>istream& operator>>(istream& s, const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>Reads z from the stream s, in the form(real, imaginary). </dd> </dl> <hr> <h2>Complex Functions</h2> The complex functions are unique to the complex type and do not overload names of the ANSI C math library. <hr> <h2><a name="arg">arg</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>double arg(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>The arg function determines the angle, in radians, of the number in<br> the complex plane specified in the x argument. The positive real axis<br> has angle 0; the positive imaginary axis has angle pi/2. <p> The arg function is equivalent to: <pre> atan2(imag(x), real(x)) </pre> </dd> </dl> <dt><strong>Return Value</strong></dt> <dd>Returns the argument of the complex number z in radians. </dd> <hr> <h2><a name="imag">complex::imag, complex::real</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>double& complex::imag();<br> double& complex::real(); </tt></dd> <dt><strong>Description</strong></dt> <dd>complex::imag returns the imaginary portion of a complex number; complex::real returns the real portion. Either function can be on the left side or right side of an assignment statement. </dd> <dt><strong>Example</strong></dt> <dd><pre>For complex::imag For complex::real #include <oldcomplex.h> #include <oldcomplex.h> complex z1(1.0,2.0), z2; complex z1(1.0,2.0), z2; z1.imag() = z2.imag(); z1.real() = z2.real(); </pre> </dd> </dl> <hr> <h2><a name="conj">conj</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex conj(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the complex conjugate of a complex number. If the complex number z is x+iy, then conj(z) is x-iy. </dd> </dl> <hr> <h2><a name="imag">imag</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>double imag(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the imaginary portion of a complex number. It can be on only the right side of an assignment statement. </dd> </dl> <hr> <h2><a name="modulus">modulus</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>double modulus(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the absolute value of a complex number. The absolute value of a complex number is also called the modulus. modulus(z) is equal to abs(z), which is sqrt (x * x + y * y). </dd> </dl> <hr> <h2><a name="norm">norm</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>double norm(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the square of the absolute value of a complex number. For z, of form (x + iy), conj(z) = (x * x + y * y). </dd> </dl> <hr> <h2><a name="polar">polar</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex polar(double range, double theta); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the complex number that is the result of converting polar coordinates range and theta to x and y coordinates. This is equivalent to using the formula: <pre>complex(range * cos(theta), range * sin(theta)); </pre> </dd> </dl> <hr> <h2><a name="real">real</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>double real(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the real portion of a complex number. It can be on only the right side of an assignment statement. </dd> </dl> <hr> <h2>Trigonometric and hyperbolic functions</h2> The trigonometric and hyperbolic functions overload the names of ANSI C library floating-point trigonometric and hyperbolic functions.<p> <hr> <h2><a name="acos">acos</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex acos(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the arccosine of a complex number. </dd> </dl> <hr> <h2><a name="complex_asin">asin, asinh</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex asin(const complex& z);<br> complex asinh(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>asin returns the arcsine of a complex number. asinh returns the hyperbolic arcsine of a complex number. </dd> </dl> <hr> <h2><a name="complex_atan">atan, atanh</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex atan(const complex& z);<br> complex atanh(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>atan returns the arctangent of a complex number. atanh returns the hyperbolic arctangent of a complex number. </dd> </dl> <hr> <h2><a name="complex_cos">cos, cosh</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex cos(const complex& z);<br> complex cosh(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>cos returns the cosine of a complex number. cosh returns the hyperbolic cosine of a complex number. </dd> </dl> <hr> <h2><a name="complex_sin">sin, sinh</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex sin (const complex& z);<br> complex sinh(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>sin returns the sine of a complex number. sinh returns the hyperbolic sine of a complex number. </dd> </dl> <hr> <h2><a name="complex_tan">tan, tanh</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex tan(const complex& z);<br> complex tanh(const complex& z); </tt></dd> <dt><strong>Description</strong></dt> <dd>tan returns the tangent of a complex number. tanh returns the hyperbolic tangent of a complex number. </dd> </dl> <hr> <h2>Mathematical functions</h2> The mathematical functions overload functions contained in the ANSI C math library to provide consistent complex support. <hr> <h2><a name="abs">abs</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>double abs(const complex&); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the absolute value of a complex number. </dd> </dl> <hr> <h2><a name="exp">exp</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex exp(const complex&); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the value of e raised to a complex number. </dd> </dl> <hr> <h2><a name="complex_log">log, log10</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex log(const complex&);<br> complex log10(const complex&); </tt></dd> <dt><strong>Description</strong></dt> <dd>log returns the logarithm base e of a complex number. log10 returns the logarithm base 10 of a complex number. </dd> </dl> <hr> <h2><a name="pow">pow</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex pow(const complex&, double);<br> complex pow(const complex&, const complex &);<br> complex pow(double, const complex&);<br> complex pow(const complex&, int); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns any number raised to a complex number or vice versa. </dd> </dl> <hr> <h2><a name="sqrt">sqrt</a> </h2><dl> <dt><strong>Header</strong></dt> <dd>oldcomplex.h</dd> <dt><strong>Prototype</strong></dt> <dd><tt>complex sqrt(const complex&); </tt></dd> <dt><strong>Description</strong></dt> <dd>Returns the square root of a complex number. </dd> </dl> </div> <div id="footernav"> <a href="https://www.digitalmars.com/" title="digitalmars.com">Home</a> | <a href="/index.cgi/speech/https://digitalmars.com/rtl/../ctg/ctg.html" title="Compiler and Tools Guide">Compiler & Tools</a> | <a href="/index.cgi/speech/https://digitalmars.com/rtl/../ugr/ugr.html" title="IDDE Reference">IDDE Reference</a> | <a href="/index.cgi/speech/https://digitalmars.com/rtl/../stl/index.html" title="Standard Template Library">STL</a> | <a href="https://www.digitalmars.com/advancedsearch.html" title="Search Digital Mars web site">Search</a> | <a href="https://www.digitalmars.com//download/freecompiler.html" title="download C++">Download</a> | <a href="https://www.digitalmars.com/NewsGroup.html" title="Forums">Forums</a> </div> <div id="copyright"> Copyright © 1999-2018 by Digital Mars ®, All Rights Reserved | Page generated by <a href="https://dlang.org/spec/ddoc.html">Ddoc</a>. </div> </div><div class="naked_ctrl"> <form action="/index.cgi/speech" method="get" name="gate"> <p><a href="http://altstyle.alfasado.net">AltStyle</a> によって変換されたページ <a href="https://digitalmars.com/rtl/oldcomplex.html">(->オリジナル)</a> / <label>アドレス: <input type="text" name="naked_post_url" value="https://digitalmars.com/rtl/oldcomplex.html" size="22" /></label> <label>モード: <select name="naked_post_mode"> <option value="default">デフォルト</option> <option value="speech" selected="selected">音声ブラウザ</option> <option value="ruby">ルビ付き</option> <option value="contrast">配色反転</option> <option value="larger-text">文字拡大</option> <option value="mobile">モバイル</option> </select> <input type="submit" value="表示" /> </p> </form> </div> </body> </html>