Question

The number of complex number z such that \2 – 1\ =\z + 11 = \z – iſ equals

Answer 1

Answer

z−i∣=∣z−1∣=∣z+1∣

Letz=x+iy

∣x+i(y−1)∣=∣(x−1)+iy∣=∣(x+1)+iy∣

meanspoint(x,y)isequidistant

from(1,0),(−1,0)and(0,1)

andinthiscaseonlyapoint(0,0)

existwhichwillbeequidistantfrom