How can you use trigonometric functions to simplify $6 e^{\frac{3 π}{8} i}$ $6 e^( ( 3 pi)/8 i )$ into a non-exponential complex number?

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Answer 1 · 2016-01-02T10:49:31

By using Euler's formula.

$6*e^((3π)/8i)=2.2961+5.5433i$

Euler's formula states that:

$e^(ix)=cosx+isinx$

Therefore:

$6*e^((3π)/8i)=6*(cos((3π)/8)+i*sin((3π)/8))=$
$=6*(0.3827+0.9239i)=$
$=6*0.3827+6*0.9239i=2.2961+5.5433i$

How can you use trigonometric functions to simplify 6 e^( ( 3 pi)/8 i ) 6e3π8i 6 e^( ( 3 pi)/8 i ) into a non-exponential complex number?