I barely understand what this question is asking. excuse my ignorance if this is totally wrong, but isn't z just constant ? as it is the perimeter of a fixed triangle. I am a bit lost on this.The vertices O, A, B of a triangle in the Argand diagram are the points corresponding to the numbers 0, 1 , 1 + i respectively. Show that when the point z describes the perimeter of the triangle OAB, then locus of the points $\displaystyle z^2$ consists of part of the real axis part of a parabola and part of the imaginary axis. Sketch this locus.

[FP3 review exercise question 51]

Bobak