Solution
= Solution
Write $z=x+iy$. The <complex modulus> condition is equivalent to $(x-1)^2+y^2=4$. Thus the locus is a \b[<circle> of radius two centred at $(1,0)$] in the <complex plane>. Its extreme points are $(-1,0)$, $(3,0)$, and $(1,\pm2)$.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-2-complex-circle.png]
{title=Circle in the complex plane with centre one and radius two}