@@ -39,6 +39,38 @@ a vector on a diagram called an *Argand diagram*, representing the *complex plan
3939imaginary, together form a complex, just like a building complex (buildings
4040joined together).
4141
42+ ## Polar Form
43+ 44+ An alternative way of defining a point ` P ` in the complex plane, other than using
45+ the x- and y-coordinates, is to use the distance of the point from ` O ` , the point
46+ whose coordinates are ` (0, 0) ` (the origin), together with the angle subtended
47+ between the positive real axis and the line segment ` OP ` in a counterclockwise
48+ direction. This idea leads to the polar form of complex numbers.
49+ 50+ ![ Polar Form] ( https://upload.wikimedia.org/wikipedia/commons/7/7a/Complex_number_illustration_modarg.svg )
51+ 52+ The * absolute value* (or modulus or magnitude) of a complex number ` z = x + yi ` is:
53+ 54+ ![ Radius] ( https://wikimedia.org/api/rest_v1/media/math/render/svg/b59629c801aa0ddcdf17ee489e028fb9f8d4ea75 )
55+ 56+ The argument of ` z ` (in many applications referred to as the "phase") is the angle
57+ of the radius ` OP ` with the positive real axis, and is written as ` arg(z) ` . As
58+ with the modulus, the argument can be found from the rectangular form ` x+yi ` :
59+ 60+ ![ Phase] ( https://wikimedia.org/api/rest_v1/media/math/render/svg/7cbbdd9bb1dd5df86dd2b820b20f82995023e566 )
61+ 62+ Together, ` r ` and ` φ ` give another way of representing complex numbers, the
63+ polar form, as the combination of modulus and argument fully specify the
64+ position of a point on the plane. Recovering the original rectangular
65+ co-ordinates from the polar form is done by the formula called trigonometric
66+ form:
67+ 68+ ![ Polar Form] ( https://wikimedia.org/api/rest_v1/media/math/render/svg/b03de1e1b7b049880b5e4870b68a57bc180ff6ce )
69+ 70+ Using Euler's formula this can be written as:
71+ 72+ ![ Euler's Form] ( https://wikimedia.org/api/rest_v1/media/math/render/svg/0a087c772212e7375cb321d83fc1fcc715cd0ed2 )
73+ 4274## Basic Operations
4375
4476### Adding
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