Find the locus of zzz such that Re(z)=3\text{Re}(z) = 3Re(z)=3.
Vertical line through (3,0)(3, 0)(3,0)
Horizontal line through (0,3)(0, 3)(0,3)
Circle ∣z∣=3|z| = 3∣z∣=3
Half-plane to the right of x=3x = 3x=3