= Solution
The modulus equation says that $z$ has fixed distance eight from $-1-i$. Thus its locus is \b[a circle of radius eight centered at $(-1,-1)$], with Cartesian equation $(x+1)^2+(y+1)^2=64$.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1-complex-loci.png]
{title=The original circle, a horizontal stretch, a translation and a quarter-turn}
{description=Original complex-plane loci. The map $u=2x+iy$ stretches only the horizontal coordinate; $v=z+4+3i$ translates the circle; $w=iv$ rotates that translated circle about the origin. Marked dots show each center.}
Back to article page
