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How can you use trigonometric functions to simplify # 4 e^( ( 4 pi)/3 i ) # into a non-exponential complex number?

1 Answer

Apr 22, 2016

#-2-3.464i#

Explanation:

Euler's formula says that

#e^(ix)=cosx+isinx#.

Inserting the value #x=(4pi)/3# in the equation from the question and solve

#e^((4pi)/3i)=cos((4pi)/3)+isin((4pi)/3)#
#=cos240+isin240#
#=-0.5-0.866i#

Multiply all of this by #4# to give the final answer

#4e^((4pi)/3i)=-2-3.464i#

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