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- Thread starter solitude
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I would expect you to do better than that if I were your teacher. Are you familiar with polar coordinate representation of complex numbers (e.g., https://en.wikipedia.org/wiki/Complex_number#Polar_complex_plane) ?View attachment 29892

should I put like -(1/2+i sqrt(3)/2)^35 here

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This looks like a typo: cos(t/35) + isin(t/35) -- should not it be cos(35t)+i*sin(35t) ?Can you explain why the minus appeared outside?

Hint: e^{it}= cos(t) + i sin(t) and [cos(t) + isin(t)]^{35}= cos(t/35) + isin(t/35)

You need to find t such that cos(t) = 1/2 and cos(t) = sqrt(3)/2

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With all this type of question we first need the argument.View attachment 29892

should I put like -(1/2+i sqrt(3)/2)^35 here

If [imath]z= \left( {\dfrac{1}{2} -{\bf i}\dfrac{{\sqrt 3 }}{2}} \right)[/imath] then so that [imath]\arg(z)=-\dfrac{\pi}{3}~\&~|z|=1[/imath]. What is [imath]z^{35}=?[/imath]