Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Possible Duplicate:
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 $z\in\mathbb{C}$?

share|improve this question

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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

add comment

1 Answer

up vote 2 down vote accepted

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

share|improve this answer
    
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
1  
@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
1  
$\cos(\pi/5) = (1+\sqrt{5}\,)/4$. –  GEdgar Dec 20 '11 at 20:27
add comment

Not the answer you're looking for? Browse other questions tagged or ask your own question.