Zadanie 2b, Paper 3, maj 2026, TZ1, Matematyka AA IB HL

In a complex-plane path model, $z=r(\cos\theta+i\sin\theta)$ with r≥0. Investigate the family $r=a+b\cos\theta$. Use $x=\operatorname{Re}z=r\cos\theta$ and $y=\operatorname{Im}z=r\sin\theta$. Angles are in radians; the origin is included whenever r=0 even though its complex argument is undefined.