Answer to Question #346624 in Complex Analysis for Busi

Question

Convert (1−i)/2 into trigonometric form

Answer 1

$$z=\dfrac{1}{2}-\dfrac{1}{2}i$$

Quadrant IV

$$r^2=(\dfrac{1}{2})^2+(-\dfrac{1}{2})^2=\dfrac{1}{2}$$

$$r=\dfrac{\sqrt{2}}{2}, \theta=\tan^{-1}(\dfrac{-(1/2)}{1/2})+2\pi=\dfrac{7\pi}{4}$$

$$(\dfrac{\sqrt{2}}{2}, \dfrac{7\pi}{4})$$

Or

$$r=\dfrac{\sqrt{2}}{2}, \theta=\tan^{-1}(\dfrac{-(1/2)}{1/2})+\pi=\dfrac{3\pi}{4}$$

$$(-\dfrac{\sqrt{2}}{2}, \dfrac{3\pi}{4})$$