Question

Let z = 8e^(5iπ/6)
Write z^6 in the form of a+bi

this is what I got, 8^6(cos(20Ï€/3)+isin(20Ï€/3))
is it correct?

Answer 1

no i don't think so

Answer 2

the \(8^6\) part is right, your last job is to multiply the angles by 6

Answer 3

\[z = 8e^{\frac{5iπ}{6}\]
\[z^6=( 8e^{\frac{5iπ}{6})^6\]
\[=8^6e^{5p\pi}\]

Answer 4

\[z = 8e^{\frac{5i\pi}{6}}\]
\[z^{6} = 8e^{5i\pi} = 8(e^{i\pi})^{5}\]
\[ = 8(-1)^{5} = -8\]

Answer 5

\[z = 8e^{\frac{5iπ}{6}}\]

Answer 6

oh oops i found my mistake, I was multiplying the angle by 8..

Answer 7

\[z^6 = (8e^{\frac{5iπ}{6}}^6=8^6e^{5\pi i}\]

Answer 8

WE MUSN'T FORGET
\[e^{i\pi} = -1 \]
(therefore god exists)

Answer 9

in anycase even though i cannot see what i am writing, you should get
\[8^6(\cos(5\pi)+i\sin(5\pi))\]

Answer 10

Oh, wait, I probably mean
\[-8^{6} = -2^{18}\]

Answer 11

man is this slow \(-8^6\) is your answer

Answer 12

yep that's what I got thanks :)