1. Find (2+2i)^8 in Cartesian form
2. Square roots of -i
3. Show the following graphically |z+1|=|z-1| (abs value)
I am lost on 1 but my answer for 2 is i, sqrt(1-i)/2
as for 3, is it just a unit circle?
2) Suppose . Equating real and imaginary parts gives |a|=|b| and ab=-1/2. The (two!) solutions are then and .
3) This is the set of points z whose distance from 1 is the same as their distance from -1. The locus of points equidistant from two points is a straight line perpendicular to the line joining the two points and passing through its midpoint. In this case, it is the line on the imaginary axis.