If z1 =2cis120, z2=4cis20, and z1/z2=a+bi, then a = and b = ?

Question

asked Aug 18, 2020 180k views

2 Answers

Kaan Burak Sener · Answer 1 · 2020-08-23T12:24:50+0000

Hello from MrBillDoesMath!

Answer:

a = 0, b = 1/2

Discussion:

z1 = 2 cis120, z2 = 4 cis30

NOTE: The question states z2 = 4cis20 but the image shows 4cis30. I'm using the values shown in the image.

z1/z2 =

2 cis120 / 4 cis30 =

(2/4) cis(120-30) =

(1/2) cis(90) =

(1/2) (cos90 + i sin90) = => as cos90 = 0 and sin90 =1

(1/2) (0 + i) =

0 + (1/2) i

If z1/z2 = a + bi, then a = 0. and b = 1/2

Thank you,

MrB