Question

How can you use trigonometric functions to simplify `2 e^( ( pi)/8 i )` into a non-exponential complex number?

Answer 1

`1.8478+0.7654i`

Explanation:

We can use the identity `re^(itheta)=rcostheta+irsintheta`

Hence, `2e^(pi/8i)=2cos(pi/8)+2sin(pi/8)i`

= `2xxsqrt(2+sqrt2)/2+2xxsqrt(2-sqrt2)/2i`

or in decimal notation approximately

= `2xx0.9239+2xx0.3827i`

= `1.8478+0.7654i`