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How do I find the principal argument of the principal $5$th root of $z$ when $z = 4 + 7i$?

I have got the answer as $11$; is that right or I did a mistake?

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  • $\begingroup$ Yes. What I did was getting it in the polar form. sqrt 65 (cos 60.255 + i sin 60.255) = 11.000. Is my steps right or totally wrong? $\endgroup$ – aD1234567890 Feb 19 '14 at 1:45
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$$r\cos\theta=4\\r\sin\theta=7\\\tan\theta=7/4\\\theta=\tan^{-1}(7/4)\\\theta/5\approx12^\circ$$

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