Question

How can you use trigonometric functions to simplify `25 e^( ( 2 pi)/3 i )` into a non-exponential complex number?

Answer 1

`25e^((2pi)/3 i )=-25/2+25isqrt3 /2`

Explanation:

`re^(itheta)=r(cos theta+i sin theta)`
`25e^((2pi)/3 i )->r=25, theta=((2pi)/3)`
`25e^((2pi)/3 i )=25(cos ((2pi)/3) + i sin ((2pi)/3))`
`25e^((2pi)/3 i )=25cos ((2pi)/3) + 25i sin ((2pi)/3)`
`25e^((2pi)/3 i )=-25/2+25isqrt3 /2`