Hi, how do you do this Q?
The pt P in an argand dig represents the variable complex no z and the pt A in the first quadrant represents the fixed complex no a. Draw on the same dig, the pt A and the locus of P for the following cases:
a) |z-a| = |a|
b) arg (z-a) = arg (a) + (pie/2)
Hence, find a value of a such that the complex no z satisfying both eqns in part a) and b) is purely imaginary.