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Loser66
 one year ago
Find real and imaginary part of \((\dfrac{1i\sqrt3}{2})^6\) by polar expression.
Please, help
Loser66
 one year ago
Find real and imaginary part of \((\dfrac{1i\sqrt3}{2})^6\) by polar expression. Please, help

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.1oh, I know what is wrong, it should be \(z = 1 e^{i4\pi/3}\) right?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\((\dfrac{1i\sqrt3}{2})^6\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Yesdw:1441922670446:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/widgets/view.jsp?id=47e6fd9e600778e368177b1edd70b025

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0idk why i typed this :O

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and @Loser66 the polar form is the one with cosine and sine not exponential Form

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1But we can find the real part and imaginary part by polar, right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1As above, I have \(z = e^{4i\pi/3}\) , then \(z^6 = e^{i8\pi}= cos (8\pi) + isin(8\pi)\) Hence R(z) =1 and Im (z) =0, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah sure \( (x+iy)^n=(r\cos n \theta+i r \sin n \theta) \)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\[(\dfrac{1i\sqrt3}{2})^6\] \[= (\frac{1}{2} i\frac{\sqrt{3}}{2})^6\] \[=(e^{i \frac{4 \pi}{3}})^6\] \[=e^{i 8 \pi} = 1\]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1find the 6 sixth roots of 1, next that's more frustrating.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441924027440:dw
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