Answer to Question #348734 in Math for Simon

Question

Convert 1-i / 2 into trigonometric form

Answer 1

$$r^2=x^2+y^2=(1)^2+(-\dfrac{1}{2})^2=\dfrac{5}{4}$$

$$\tan\theta=\dfrac{y}{x}=\dfrac{-1/2}{1}=-\dfrac{1}{2}$$

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

Quadrant IV

$$r=\dfrac{\sqrt{5}}{2}, \theta=2\pi-\tan^{-1}(\dfrac{1}{2})$$

or

$$r=-\dfrac{\sqrt{5}}{2}, \theta=\pi-\tan^{-1}(\dfrac{1}{2})$$