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

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

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Answer 1 · 2016-02-23T20:56:59

$3 (cos (\frac{π}{8}) + i sin (\frac{π}{8}))$ $3(cos(pi/8) + isin(pi/8))$

Explanation:

Using $Euler's relation$ $color(blue)" Euler's relation"$

which states: $r e^{i θ} = r (cos θ + i sin θ)$ $re^(itheta) = r(costheta + isintheta )$

here r = 3 and $θ = \frac{π}{8}$ $theta = pi/8$

$\Rightarrow 3 e^{\frac{π}{8} i} = 3 (cos (\frac{π}{8}) + i sin (\frac{π}{8}))$ $rArr 3e^(pi/8i) = 3(cos(pi/8) + isin(pi/8))$

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

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