Question

If |z|=2 then points representing the complex numbers -1+5z will lie on a
1) circle
2) straight line
3) parabola
4) ellipse

Answer 1

Hi,

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 = 10²
which is an equation of a circle.