Question

if 3-3i and z2=7(cos(5pi/9)+isin(5pi/9)) then z1/z2=?? PLEASE HELP :)

Answer 1

A) 21(cos(25pi/36)+i sin(25pi/36))
B) 21sqrt2(cos(29pi/36)+i sin(29pi/36))
C) 3sqrt2/7(cos(29pi/36)+i sin(29pi/36))
D) 3sqrt2/7(cos(-11pi/36)+i sin(-11pi/36))

Answer 2

\[\frac{z _{1}}{z _{2}}=\frac{r _{1}e ^{i \theta _{1}}}{r _{2}e ^{i\ \theta _{2}}}=\frac{r _{1}}{r _{2}}e ^{i(\theta _{1}}-\theta _{2})\]

Answer 3

which one of the options do you think it is?

Answer 4

You need to put z1 and z2 into exponential form and then use the equation above.
z1 has to be converted to polar form.
\[r=\sqrt{(3^{2}}+3^{2})=\sqrt{18}\]
\[\tan \theta=\frac{-1}{1}=-1\]
Can you now put z1 into the form\[z _{1}=r \cos \theta+ir \sin \theta\]

Answer 5

I did, I got D as an answer but I'm not sure it's correct..

Answer 6

do you agree on D?

Answer 7

@kropot72

Answer 8

No. D is not the correct choice.

Answer 9

well then I did something wrong. lol

Answer 10

C?

Answer 11

I already gave you what is needed for 'r' of the answer.
\[r=\frac{z _{1}}{z _{2}}=\frac{\sqrt{18}}{7}=\frac{3\sqrt{2}}{7}\]
So the only remaining choice is obvious.

Answer 12

actually the correct answer was D. -.-