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Question

Let f(z)=sinz and g(z)=cosz. If * denotes a composition of function then show that (f+ig)(fig)=ieeiz.

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Solution

(fig)(z)=f(z)ig(z)=sinzicosz=i(cosz+sinz)=ieiz
(f+ig)(fig)(z)=(f+ig)(ieiz)=f(ieiz)+ig(ieiz)
=sin(ieiz)+icos(eiz)
=iei(ieiz)=ieeiz

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