De Moirve's Theorem (1 Viewer)

teanido

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1 - cos pi/7 + i sin pi/7
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1 - cos pi/7 - i sin pi/7

How to simplify that?

Whoops, wait, the whole thing is to the power of 7...
 
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jyu

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teanido said:
1 - cos pi/7 + i sin pi/7
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1 - cos pi/7 - i sin pi/7

How to simplify that?
Multiply top and bottom by the conjugate of the bottom.
Expand and simplify using sinsq + cossq =1.
Factorise and cancel common factor (2 - 2cos(pi/7)) to obtain -cos(pi/7) + isin(pi/7)

:santa:
 

teanido

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... Guess I wasn't thinking today, wrote out the question above wrong, tomorrow got a major 2 hour exam on curve sketching and complex numbers..
 

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