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Add polar form of complex number to README.
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@ -39,6 +39,38 @@ a vector on a diagram called an *Argand diagram*, representing the *complex plan
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imaginary, together form a complex, just like a building complex (buildings
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imaginary, together form a complex, just like a building complex (buildings
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joined together).
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joined together).
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## Polar Form
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An alternative way of defining a point `P` in the complex plane, other than using
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the x- and y-coordinates, is to use the distance of the point from `O`, the point
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whose coordinates are `(0, 0)` (the origin), together with the angle subtended
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between the positive real axis and the line segment `OP` in a counterclockwise
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direction. This idea leads to the polar form of complex numbers.
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The *absolute value* (or modulus or magnitude) of a complex number `z = x + yi` is:
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The argument of `z` (in many applications referred to as the "phase") is the angle
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of the radius `OP` with the positive real axis, and is written as `arg(z)`. As
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with the modulus, the argument can be found from the rectangular form `x+yi`:
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Together, `r` and `φ` give another way of representing complex numbers, the
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polar form, as the combination of modulus and argument fully specify the
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position of a point on the plane. Recovering the original rectangular
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co-ordinates from the polar form is done by the formula called trigonometric
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form:
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Using Euler's formula this can be written as:
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## Basic Operations
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## Basic Operations
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### Adding
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### Adding
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