De Moirve's Theorem (1 Viewer)

[teanido]

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

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

How to simplify that?

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

 

[jyu]

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

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)

 

[teanido]

... 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..

 

[blackfriday]

easy topics no sweat.