Question

Find the quotient of z1 by z2. Express your answer in trigonometric form.
z1 = 4(cos(pi/3) + isin(pi/3))
z2 = 3(cos(2pi/5) + isin(2pi/5))

A. 4/3(cos(-pi/15) + isin(-pi/15))
B. 12(cos(-pi/15) + isin(-11pi/15))
C. 12(cos(11pi/15) + isin(11pi/15))
D. 4/3(cos(11pi/15) + isin(11pi/15))

Answer 1

@hartnn

Answer 2

What tells me that you have the Euler's Formula involved?

Answer 3

the what? :/

Answer 4

Never mind. Actually no, it's pretty simple:\[\large e^{ix}=\cos(x) + i\sin(x)\]

Answer 5

how does that help me?

Answer 6

ello..?

Answer 7

Not sure enough.

Answer 8

say what

Answer 9

@ZeHanz perhaps you can help?

Answer 10

\[\Large z_{1} = 4e^{i \pi/3}, z_{2} = 3e^{i2\pi/5}\]
\[\Large z_{1}/z_{2} = \frac{4e^{i \pi/3}}{3e^{i2\pi/5}} = \frac{4}{3}e^{i(\pi/3 - 2\pi/5)}\]
\[\Large = \frac{4}{3}e^{-i\pi/15} = \frac{4}{3}(\cos{\frac{-\pi}{15}}+i\sin{\frac{-\pi}{15}})\]

Hence (A)

Answer 11

@Spectrum: I think @FoolAroundMath did a pretty good job!

Answer 12

well i tbh would have considered it foolish to accept that answer with out letting you have your say and it said you were still typing ..but ty

Answer 13

Thank you for that!