Prove this compex number problem

Prove that {{cosÎ¸+sinÏ†)+i(sinÎ¸-cosÏ†)}ⁿ+{(cosÎ¸+sinÏ†)-i(sinÎ¸-cosÏ†)}ⁿ
=2ⁿ⁺¹cosⁿ(Ï€/4 +Î¸-Ï†/2) cos[n(Ï€/4 -Î¸+Ï†/2)]

2 Answers

{cosÎ¸+sinÏ†)+i(sinÎ¸-cosÏ†) = e^iÎ¸-i(cosÏ†+isinÏ†)=e^iÎ¸-e^iÏ†

now use the same for (cosÎ¸+sinÏ†)-i(sinÎ¸-cosÏ†)

and them apply binomial theorem.. :)

Thank you
:-)

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