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cexpf, cexp, cexpl

From cppreference.com
< c‎ | numeric‎ | complex
 
 
 
Complex number arithmetic
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Power and exponential functions
cexp
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Defined in header <complex.h>
float complex       cexpf( float complex z );
(1) (since C99)
double complex      cexp( double complex z );
(2) (since C99)
long double complex cexpl( long double complex z );
(3) (since C99)
Defined in header <tgmath.h>
#define exp( z )
(4) (since C99)
1-3) Computes the complex base-e exponential of z.
4) Type-generic macro: If z has type long double complex , cexpl is called. if z has type double complex , cexp is called, if z has type float complex , cexpf is called. If z is real or integer, then the macro invokes the corresponding real function (expf, exp , expl). If z is imaginary, the corresponding complex argument version is called.

Contents

[edit] Parameters

z - complex argument

[edit] Return value

If no errors occur, e raised to the power of z, \(\small e^z\)ez
 is returned.

[edit] Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

  • cexp(conj (z)) == conj (cexp(z))
  • If z is ±0+0i, the result is 1+0i
  • If z is x+∞i (for any finite x), the result is NaN+NaNi and FE_INVALID is raised.
  • If z is x+NaNi (for any finite x), the result is NaN+NaNi and FE_INVALID may be raised.
  • If z is +∞+0i, the result is +∞+0i
  • If z is -∞+yi (for any finite y), the result is +0cis(y)
  • If z is +∞+yi (for any finite nonzero y), the result is +∞cis(y)
  • If z is -∞+∞i, the result is ±0±0i (signs are unspecified)
  • If z is +∞+∞i, the result is ±∞+NaNi and FE_INVALID is raised (the sign of the real part is unspecified)
  • If z is -∞+NaNi, the result is ±0±0i (signs are unspecified)
  • If z is +∞+NaNi, the result is ±∞+NaNi (the sign of the real part is unspecified)
  • If z is NaN+0i, the result is NaN+0i
  • If z is NaN+yi (for any nonzero y), the result is NaN+NaNi and FE_INVALID may be raised
  • If z is NaN+NaNi, the result is NaN+NaNi

where \(\small{\rm cis}(y)\)cis(y) is \(\small \cos(y)+{\rm i}\sin(y)\)cos(y) + i sin(y)

[edit] Notes

The complex exponential function \(\small e^z\)ez
 for \(\small z = x + {\rm i}y\)z = x+iy equals \(\small e^x {\rm cis}(y)\)ex
 cis(y), or, \(\small e^x (\cos(y)+{\rm i}\sin(y))\)ex
 (cos(y) + i sin(y))

The exponential function is an entire function in the complex plane and has no branch cuts.

[edit] Example

Run this code
#include <stdio.h>
#include <math.h>
#include <complex.h>
 
int main(void)
{
 double PI = acos (-1);
 double complex z = cexp(I * PI); // Euler's formula
 printf ("exp(i*pi) = %.1f%+.1fi\n", creal (z), cimag (z));
 
}

Output: 

exp(i*pi) = -1.0+0.0i

[edit] References

  • C11 standard (ISO/IEC 9899:2011):
  • 7.3.7.1 The cexp functions (p: 194)
  • 7.25 Type-generic math <tgmath.h> (p: 373-375)
  • G.6.3.1 The cexp functions (p: 543)
  • G.7 Type-generic math <tgmath.h> (p: 545)
  • C99 standard (ISO/IEC 9899:1999):
  • 7.3.7.1 The cexp functions (p: 176)
  • 7.22 Type-generic math <tgmath.h> (p: 335-337)
  • G.6.3.1 The cexp functions (p: 478)
  • G.7 Type-generic math <tgmath.h> (p: 480)

[edit] See also

(C99)(C99)(C99)
computes the complex natural logarithm
(function) [edit]
(C99)(C99)
computes e raised to the given power (\({\small e^x}\)ex)
(function) [edit]
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