Question

Complex numbers help. Will give medal and fan. *Question attached below*

Answer 1

Simplify, without the use of tables

Can I have a step by step explanation? I'm thinking de Moivre's theorem should be applied here?

Answer 2

ok convert
cos(1/(7 pi) ) - i sin (1/(7 pi) )
to e^(r theta )
can u do it ?

Answer 3

Oh no, I am not familiar with how to convert to exponential form :O

Answer 4

use this formula :-
\(\Huge r\cos \theta -ri\sin \theta =e^{ri\theta }\)
\(\Huge \cos \frac{\pi}{7 }-i\sin \frac{\pi}{7 }=e^{\frac{-i\pi}{7}}\)
\(\Huge \cos \frac{\pi}{7 }+i\sin \frac{\pi}{7 }=e^{\frac{i\pi}{7}}\)

Answer 5

typo
this is the formulla
\(\Huge r\cos \theta +ri\sin \theta =e^{ri\theta }\)

Answer 6

so lets continue
\(\large \frac{( \cos \frac{\pi}{7 }-i\sin \frac{\pi}{7 })^3}{( \cos \frac{\pi}{7 }+i\sin \frac{\pi}{7 })^4}\\\large =\frac{ ( e^{\frac{ -i\pi}{7}})^3 }{ ( e^{\frac{ i\pi}{7}})^4 } \)

Answer 7

\(\Huge \frac{( \cos \frac{\pi}{7 }-i\sin \frac{\pi}{7 })^3}{( \cos \frac{\pi}{7 }+i\sin \frac{\pi}{7 })^4}\\\Huge =\frac{ ( e^{\frac{ -i\pi}{7}})^3 }{ ( e^{\frac{ i\pi}{7}})^4 } \)

Answer 8

got it ?!
the rest is arithmatic :o
let me know if u still stuck in something

Answer 9

I think I get it. So I just divide now, right?

Answer 10

yes

Answer 11

like this
\(\Huge \frac{ ( e^{\frac{ -i\pi}{7}})^3 }{ ( e^{\frac{ i\pi}{7}})^4 }= \frac{ e^{\frac{ -i3\pi}{7}} }{ e^{\frac{ i4\pi}{7}} }\)

Answer 12

Alrighty :) Thank you!

Answer 13

np :)