Wednesday, July 31, 2019

trigonometry - Is Euler's formula valid for complex arguments



I found this question here :



Evaluate cos(z), given that z=ilog(2+3)



It says that -
eiz=cos(z)isin(z)


isn't necessarily true because sinz
is imaginary (for the particular value of z in the link). But, the proof of Euler's formula using Maclaurin series suggests that it should be valid for complex arguments too. What am I missing?



Answer



No, it doesn't say that eiz=cos(iz)isin(iz)

is not necessarily true! It is true. What it says in that other answer is that cos(iz) is not necessarily the real part of eiz.


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