$(z+\frac{i}{2})^3-i=0$
Just got this problem on my Complex Variables hw and have no idea how to go about it. I know how to solve things like $z^n=w$, roots of unity etc but the $\frac{i}{2}$ is really throwing me off. Thanks!
Complex variables: solve for roots of $(z+\frac{i}{2})^3-i=0$
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complex-analysis
complex-numbers
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1Hint: let $w = z+\frac i2$. – 2017-01-24
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0It's sufficient that after finding solutions $z^3=i$ add $-\dfrac{i}{2}$ to them. – 2017-01-24
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0Calculate all three cubic roots of i. Then equate each of them to $z+\frac{i}{2}$. – 2017-01-24
1 Answers
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HINT
Let
$$z+\frac{i}{2}=w$$
and notice that $$w^3=i, \bar{w}^3=-i$$