How can you use trigonometric functions to simplify # 15 e^( ( 2 pi)/3 i ) # into a non-exponential complex number?

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Answer 1 · 2017-11-19T13:27:05

The answer is #=15/2(-1+isqrt3)#

Apply Euler's formula

#e^(itheta)=costheta+isintheta#

Therefore,

#15e^(2/3pii)=15(cos(2/3pi)+isin(2/3pi))#

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

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

So,

#15e^(2/3pii)=15(-1/2+sqrt3/2i)#

#=15/2(-1+isqrt3)#