If z1 = 1+i, Z2 = -1-i. Find z3 if z1, Z2, z3 form equilateral triangle

First represent it as coordinates and for a moment drop the i.z1=1+i so coordinates are (1,1) z2=-1-i that is (-1,-1) now take z3 as (X, y) then using dist formula (x-1)^2 +(y-1)^2 = (x+1)^2 + (y+1)^2 = 8 We get x+y=0. x^2 +y^2 = 6 We get (x,y)=(3^1/2,-3^1/2) and (-3^1/2,3^1/2)So that is z3 = 3^1/2 - i(3^1/2) and -3^1/2 + i (3^1/2)