complex numbers (1 Viewer)

[joesmith1975]

need help

b) (i) Find and describe the cartesian equation of the locus represented by |z|² = z + (conjugate z).
(ii) Sketch this locus on an argand diagram.

 

[Riviet]

let z=x+iy.
[sqrt(x²+y²)]²=(x+iy) + (x-iy)
x²+y²=2x
x²-2x+1+y²=1
(x-1)²+y²=1, which is the locus of a circle with centre (1,0) and radius 1 unit. The sketch is easy.