Functions Question 529
Question: Let $ f(z)=sinz $ and $ g(z)=cosz. $ If * denotes a composition of functions, then the value of $ {{(f+ig)}^{*}}(f-ig) $ is:
Options:
A) $ i{e^{-{e^{-iz}}}} $
B) $ i{e^{-e^{iz}}} $
C) $ -i{e^{-{e^{-iz}}}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ (f-ig)(z)=f(z)-ig(z)=sinz-icosz $ $ =-i(cosz+isinz)=-ie^{iz}=\theta (say) $ Now $ {{(f+ig)}^{*}}(f-ig)(z)=(f+ig)(f-ig)(z) $ $ =(f+ig)(\theta )=f(\theta )+ig(\theta )=sin\theta +icos\theta $ $ =i(cos\theta -isin\theta )=i{e^{-i\theta }}=i{e^{-i(-ie^{iz})}}=i{e^{-e^{iz}}} $
BETA
