How can you use trigonometric functions to simplify $2 e^{\frac{13 π}{12} i}$ $2 e^( ( 13 pi)/12 i )$ into a non-exponential complex number?

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Answer 1 · 2016-10-03T15:52:31

Use $A e^{θ i} = A cos (θ) + A sin (θ) i$ $Ae^(thetai) = Acos(theta) + Asin(theta)i$

$A e^{θ i} = A cos (θ) + A sin (θ) i$ $Ae^(thetai) = Acos(theta) + Asin(theta)i$

$2 e^{\frac{13 π}{12} i} = 2 cos (\frac{13 π}{12}) + 2 sin (\frac{13 π}{12}) i$ $2e^((13pi)/12i) = 2cos((13pi)/12) + 2sin((13pi)/12)i$

I used a calculator to compute the real and imaginary parts, they are not nice round numbers so I decided to leave you with this form.

How can you use trigonometric functions to simplify 2e13π12i 2 e^( ( 13 pi)/12 i ) into a non-exponential complex number?