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

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Answer 1 · 2016-04-22T13:17:57

$-2-3.464i$

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

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

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