How can you use trigonometric functions to simplify # 18 e^( ( 5 pi)/3 i ) # into a non-exponential complex number?

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Answer 1 · 2016-12-13T13:00:26

The answer is #=9(1-isqrt3)#

We use

#e^(itheta)=costheta+isintheta#

#cos(5/3pi)=1/2#

#sin(5/3pi)=-sqrt3/2#

#18e^(5/3ipi)=18(cos(5/3pi)+isin(5/3pi))#

#=18(1/2-isqrt3/2)#

#=9(1-isqrt3)#