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**jayshizwiz** solve $\displaystyle (1-i)^{2009}$

Attempt:

r = $\displaystyle \sqrt{2}$

tan$\displaystyle \Theta$ = -1 $\displaystyle \rightarrow$ tan$\displaystyle \Theta$ = $\displaystyle \frac{7\pi}{4}$

so...

$\displaystyle (1-i)^{2009}$ = $\displaystyle \sqrt{2}^{2009}(cis \frac{2009 \cdot 7\pi}{4})$

$\displaystyle \sqrt{2}^{2009} = \sqrt{2} \cdot 2^{1004} $

so... $\displaystyle (1-i)^{2009}$ = $\displaystyle \sqrt{2} \cdot 2^{1004}(cis \frac{2009 \cdot 7\pi}{4}) $

can someone please tell me what I do with $\displaystyle (cis \frac{2009 \cdot 7\pi}{4}) $

Thanks. I'm blanking out...