1. ## complex numbers

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!

2. Originally Posted by alexandrabel90
hi!

Could someone teach me how to solve (z-i)^6 = 64?
We know that $\sqrt[6]{{64}} = 2$. Define $\sigma _k = 2\left[ {\exp \left( {\frac{{k\pi }}{3}i} \right)} \right],\,k = 0,1 \cdots 5$

Take note: $\left( {\forall k} \right)\left[ {\left( {\sigma _k } \right)^6 = 64} \right]$.

Thus the six solutions are $z = \sigma _k + i,\,\,k = 0,1 \cdots 5$

3. and how do i find the mod of z?

4. Originally Posted by alexandrabel90
and how do i find the mod of z?
To get the modulus you will need to express in cartesian form the solutions that have been given to you.