How can you use trigonometric functions to simplify $2 e^{\frac{17 π}{12} i}$ $2 e^( ( 17 pi)/12 i )$ into a non-exponential complex number?

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Answer 1 · 2017-01-26T03:32:13

$2 [cos (\frac{17 π}{12}) + i sin (\frac{17 π}{12})]$ $2[cos ((17pi)/12)+ i sin ((17pi)/12)]$

Use Euler's formula for complex numbers $e^{i t} = cos t + i sin t$ $e^(it)= cos t +i sin t$

Accordingly $2 e^{\frac{17 π i}{12}} = 2 [cos (\frac{17 π}{12}) + i sin (\frac{17 π}{12})]$ $2e^[(17pii)/12)=2[cos ((17pi)/12)+ i sin ((17pi)/12)]$

How can you use trigonometric functions to simplify 2 e^( ( 17 pi)/12 i ) 2e17π12i 2 e^( ( 17 pi)/12 i ) into a non-exponential complex number?