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How can you find the complex roots of i?

How can I find the solutions of the equation $$(2z+1)^5-i=0,$$ over the complex numbers $z\in\mathbb{C}$?

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marked as duplicate by Jonas Meyer, Srivatsan, Asaf Karagila, Zev Chonoles Dec 20 '11 at 21:57

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Find the fifth roots of $i$, subtract $1$, and divide by $2$.

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yeah but than i have to calculate $cos(36)$ and I have to calculate it without a calculator – Some1 Dec 20 '11 at 20:23
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@Some1 It is usually considered equally acceptable to express complex numbers in "standard form" ($a+bi$), "polar form" ($r\,\mathrm{e}^{it}$) or a combination. Your roots can be expressed easily as a combination of polar and standard elements. On the other hand, trig functions of $\pi/5$ have exact values. – alex.jordan Dec 20 '11 at 20:27
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$\cos(\pi/5) = (1+\sqrt{5}\,)/4$. – GEdgar Dec 20 '11 at 20:27

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