Given z1 and z2 below. Calculate z1/z2 and write your answer in rcistheta form.

z1=-3+3sqrt (3) i

z2=27i

(2/9) cis (30°)

Step-by-step explanation:

We can express the two numbers in magnitude∠angle form, then find their ratio.

|z1| = 3√ ((-1) ² + (√3) ²) = 3√4 = 6

∠z1 = arctan ((3√3) / (-3)) = - arctan (√3) = 120°

z2 = 27∠90°

So, the ratio is ...

z1/z2 = (6∠120°) / (27∠90°) = (6/27) ∠ (120°-90°)

z1/z2 = (2/9) ∠30°