hi!
Could someone teach me how to solve (z-i)^6 = 64?
how do you go about finding the mod and the 6 answers for z?
thanks!
We know that $\displaystyle \sqrt[6]{{64}} = 2$. Define $\displaystyle \sigma _k = 2\left[ {\exp \left( {\frac{{k\pi }}{3}i} \right)} \right],\,k = 0,1 \cdots 5$
Take note: $\displaystyle \left( {\forall k} \right)\left[ {\left( {\sigma _k } \right)^6 = 64} \right]$.
Thus the six solutions are $\displaystyle z = \sigma _k + i,\,\,k = 0,1 \cdots 5$