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

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

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Answer 1 · 2016-02-19T15:06:56

we can use Euler's formula to solve the problem

Explanation:

Euler's formula $e^{i x} = cos x - i sin x$ $e^(ix)=cosx -isinx$
let $p = 3 e^{3 \frac{π}{8} i}$ $p=3e^(3pi/8i)$
$p^{2} = 9 e^{3 \frac{π}{4} i}$ $p^2=9e^(3pi/4i)$
$p^{2} = 9 e^{3 \frac{π}{4} i} = 9 (cos (3 \frac{π}{4}) + i sin (3 \frac{π}{4})$ $p^2=9e^(3pi/4i)=9(cos(3pi/4)+isin(3pi/4)$
$p = 3 \sqrt{cos (3 \frac{π}{4}) + i sin (3 \frac{π}{4})}$ $p=3sqrt(cos(3pi/4)+isin(3pi/4)$
$p = 3 \sqrt{- \frac{1}{\sqrt{2}} + i \frac{1}{\sqrt{2}}}$ $p=3sqrt(-1/sqrt(2)+i 1/sqrt(2))$

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

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