Question

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

Answer 1

`color(maroon)(=> 13.8585 + 5.7403 i`

Explanation:

Trigonometric form of `e^ (ix)`, using Euler's Equation, is given by

`e^ (ix) = cos x + i sin x`

`z = |z| e^(i x) = |z| * (cos theta + i sin theta)`

`15 e^((pi)/8i) = 15 * ( cos(pi/8) + i sin(pi/8))`

`=> 15 (0.9239 + i 0.3827)`

`color(maroon)(=> 13.8585 + 5.7403 i`