In the Argand diagram shown below the complex numbers – 1 + i, 1 + i, 1 – i, – 1 – i represent the vertices of a square ABCD. The equation of its diagonal BD is y = x. The complex number k + ki where – 1 < k < 0 represents the point E which is in the fourth quadrant and lies on the line y = x. EFGC is a square such that F lies on AB. The line GE meets the line CD produced at H such that H is represented by the complex number – 2 – i. How do I show F = -k\(k+2) + i? I've tried rotating EC and GC by i, but none seem to get the answer, nor even a fraction with k
