[JEE Advanced 1986] show that the area of the triangle on the argand diagram formed by z
Show that the area of the triangle on the Argand diagram formed by $z,\ iz,\ z+iz$ is $\tfrac12|z|^2$.
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· 2d ago
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Answer: Proved $=\tfrac12|z|^2$.
$iz$ is $z$ rotated $90^\circ$, so the two sides are perpendicular and equal to $|z|$; the right isosceles triangle has area $\frac12|z|\cdot|z|=\frac12|z|^2$.
JEE Advanced 1986 · Complex Numbers — verified solution by the Vidaara Team.
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