Question

How do you write the complex number `z = 6(cos 45° + i sin 45°)` in standard form?

Answer 1

I found: `3sqrt(2)+3sqrt(2)i`

Explanation:

We need to evaluate the values of `sin` and `cos` and multiply by `6`:
`z=6(cos(45^@)+isin(45^@))=6(sqrt(2)/2+isqrt(2)/2)=`
`=cancel(6)^3(sqrt(2)/cancel(2)+isqrt(2)/cancel(2))=3sqrt(2)+3sqrt(2)i`

which is in the form: `a+bi`