How can you use trigonometric functions to simplify $15 e^{\frac{π}{8} i}$ $15 e^( ( pi)/8 i )$ into a non-exponential complex number?

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Answer 1 · 2018-08-05T10:47:21

$\Rightarrow 13.8585 + 5.7403 i$ $color(maroon)(=> 13.8585 + 5.7403 i$

Trigonometric form of $e^{i x}$ $e^ (ix)$ , using Euler's Equation, is given by

$e^{i x} = cos x + i sin x$ $e^ (ix) = cos x + i sin x$

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$z = | z | e^{i x} = | z | \cdot (cos θ + i sin θ)$ $z = |z| e^(i x) = |z| * (cos theta + i sin theta)$

$15 e^{\frac{π}{8} i} = 15 \cdot (cos (\frac{π}{8}) + i sin (\frac{π}{8}))$ $15 e^((pi)/8i) = 15 * ( cos(pi/8) + i sin(pi/8))$

$\Rightarrow 15 (0.9239 + i 0.3827)$ $=> 15 (0.9239 + i 0.3827)$

$\Rightarrow 13.8585 + 5.7403 i$ $color(maroon)(=> 13.8585 + 5.7403 i$

How can you use trigonometric functions to simplify 15eπ8i 15 e^( ( pi)/8 i ) into a non-exponential complex number?