Add polar form of complex number to README.

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Oleksii Trekhleb 2018-08-14 23:19:30 +03:00
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@ -39,6 +39,38 @@ a vector on a diagram called an *Argand diagram*, representing the *complex plan
imaginary, together form a complex, just like a building complex (buildings imaginary, together form a complex, just like a building complex (buildings
joined together). joined together).
## Polar Form
An alternative way of defining a point `P` in the complex plane, other than using
the x- and y-coordinates, is to use the distance of the point from `O`, the point
whose coordinates are `(0,0)` (the origin), together with the angle subtended
between the positive real axis and the line segment `OP` in a counterclockwise
direction. This idea leads to the polar form of complex numbers.
![Polar Form](https://upload.wikimedia.org/wikipedia/commons/7/7a/Complex_number_illustration_modarg.svg)
The *absolute value* (or modulus or magnitude) of a complex number `z = x + yi` is:
![Radius](https://wikimedia.org/api/rest_v1/media/math/render/svg/b59629c801aa0ddcdf17ee489e028fb9f8d4ea75)
The argument of `z` (in many applications referred to as the "phase") is the angle
of the radius `OP` with the positive real axis, and is written as `arg(z)`. As
with the modulus, the argument can be found from the rectangular form `x+yi`:
![Phase](https://wikimedia.org/api/rest_v1/media/math/render/svg/7cbbdd9bb1dd5df86dd2b820b20f82995023e566)
Together, `r` and `φ` give another way of representing complex numbers, the
polar form, as the combination of modulus and argument fully specify the
position of a point on the plane. Recovering the original rectangular
co-ordinates from the polar form is done by the formula called trigonometric
form:
![Polar Form](https://wikimedia.org/api/rest_v1/media/math/render/svg/b03de1e1b7b049880b5e4870b68a57bc180ff6ce)
Using Euler's formula this can be written as:
![Euler's Form](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a087c772212e7375cb321d83fc1fcc715cd0ed2)
## Basic Operations ## Basic Operations
### Adding ### Adding