The area of the triangle with vertices A(z), B(iz), C(z+iz) is

Question

The area of the triangle with vertices $A(z), B(iz), C(z+iz)$ is

Accepted Answer

The triangle $A(z),B(iz),C(z+iz)$ has two sides $z$ and $iz$ meeting at $A$'s translate; its area equals $\dfrac12|z\cdot \overline{(iz)}	ext{ imaginary part}|=\dfrac12|z|^2$.

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