Sorry to bother you again so soon but this is another question I became stuck on.

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Consider the complex number:

$\displaystyle z = \frac {\left(\cos \frac {\pi}{4} - isin \frac {\pi}{4}\right)^2 \left(\cos \frac {\pi}{3} + isin \frac {\pi}{3}\right)^3}{\left(\cos \frac {\pi}{24} - isin \frac {\pi}{24}\right)^4}$

Find the $\displaystyle |z|$ and $\displaystyle arg z$

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Man, that LaTeX thing is hard to use!

Anyway this is what I have done so far:

$\displaystyle z = \frac {\left(\cos \frac {\pi}{4} - isin \frac {\pi}{4}\right)^2 \left(\cos \frac {\pi}{3} + isin \frac {\pi}{3}\right)^3}{\left(\cos \frac {\pi}{24} - isin \frac {\pi}{24}\right)^4}$

$\displaystyle z = \frac {\left(\frac {\sqrt 2}{2} - \frac {\sqrt 2}{2}i\right)^2 \left(\frac {1}{2} + \frac {\sqrt 3}{2}i\right)^3}{\left(\cos \frac {\pi}{24} - isin \frac {\pi}{24}\right)^4}$

No idea what $\displaystyle \frac {\pi}{24}$ is so I can't continue...

Maybe this is the wrong way - perhaps instead of tranforming them into numbers, I use cis instead:

$\displaystyle \left(\cos \frac {\pi}{3} + isin \frac {\pi}{3}\right)^3$ becomes $\displaystyle cis \frac {\pi}{3}$ and from there, use cis properties...

Anyway, this question has got me completely confused and so I'm finding it rather difficult to continue.

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Could somebody please help me please? Thanks - all help is, of course, appreciated.

PS: How do you guys manage to type up that LaTeX thing smoothly? It takes me ages to get it right! (my first time!)