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## 1.7 Polar form of Complex number

1.7.1 The unit circle: The basic trigonometric identity (i.e the Pythagorean theorem) is

Cos2θ + Sin2θ =1

It shows that the complex numbers of the form Cosθ + iSinθ

are points on the circle of radius one centered at the origin.

Cosθ + iSinθ

A point moving counter-clockwise around the circle is taken as the real number θ, moving from left to right. Similarly, the point moves clockwise if θdecreases. And whether θ increases or decreases, the point returns to the same position on the circle whenever θ changes by 2π or by 4π or by 2nπ where n is any integer.

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