Question

How do you write `1/2+5i` in polar form and find ?

Answer 1

`z = 5.025* (cos 1.47 +isin 1.47)` Angle expressed in radians.

Explanation:

In polar form `(1/2+5*i)` lies on the 1st quardrant. The length of it from the origin is `r = sqrt(.5^2+5^2) = sqrt 25.25 = 5.025` The argument is `theta=tan^-1 (5/.5) or theta = tan^-1 10 = 1.47 radian`
So in Polar form `z = 5.025* (cos 1.47 +isin 1.47)` ; If `theta` is expressed in degree then `z = 5.025* (cos 84.29 +isin 84.29)`