Question

Sum of roots of the equation $(z-1{)}^4=16$ is

Answer 1

We have,
$(z-1{)}^4=16$
$\Rightarrow z-1=(16{)}^{1/4}\cdot (1{)}^{1/4}$
$\Rightarrow z-1=2\cdot e^{i2n\pi /4},n=0,1,2,3$
$\therefore z-1=2i,-2,-2i,2$
$\Rightarrow z=1+2i,-1,1-2i,3$
Therefore, sum of roots $=4$