How can you use trigonometric functions to simplify $16 e^{\frac{π}{3} i}$ $16 e^( ( pi)/3 i )$ into a non-exponential complex number?

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Answer 1 · 2016-04-11T04:50:48

$8 + 8 \sqrt{3} i$ $8+8sqrt3i$

We can use the identity $r e^{i θ} = r cos θ + i r sin θ$ $re^(itheta)=rcostheta+irsintheta$

Hence, $16 e^{\frac{π}{3} i} = 16 cos (\frac{π}{3}) + 16 sin (\frac{π}{3}) i$ $16e^(pi/3i)=16cos(pi/3)+16sin(pi/3)i$

= $16 \times \frac{1}{2} + 16 \times \frac{\sqrt{3}}{2} i$ $16xx1/2+16xxsqrt3/2i$

= $8 + 8 \sqrt{3} i$ $8+8sqrt3i$

How can you use trigonometric functions to simplify 16eπ3i 16 e^( ( pi)/3 i ) into a non-exponential complex number?