The question:

Find the "a + ib" form of the complex numbers whose modulus and principle argument are:

|z| = 3, arg(z) = Pi/8

My attempt:

$\displaystyle 3(cos(\frac{\pi}{8}) + isin(\frac{\pi}{8}))$

I'm certain they want the solution as an exact value, so Pi/8 is going to be a pain to find. I'm thinking I have to use the double-angle formulas, but I'm doing something wrong...

$\displaystyle cos(2x) = cos^2x - sin^2x$

$\displaystyle cos (\frac{\pi}{8}) = cos^2(\frac{\pi}{16}) - sin^2(\frac{\pi}{16})$

Clearly that isn't any easier. Have any suggestions? Thanks.