If |z|=2, then the points representing the complex number -1+5z is: a)Circle b)Parabola c)Ellipse d)Straight line

It will be a circle.

Suppose z'' = -1+5z where z''=x''+iy''

=> z''+1 = 5z => |z''+1| = |5z| => |z''+1| = 5|z| => |z''+1| = 10 => (x''+1)^2 + (y'')^2 = 10^2 which is an equation of a circle.

Deepak Kumar

B.Tech, IIT Delhi.