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in Mathematics by (53.3k points)

Show that the area of the triangle on the Argand plane formed by the complex numbers z, iz and z + iz is 1/2 |z|2

1 Answer

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Best answer

We have, iz = zeiπ/2

This implies that iz is the vector obtained by rotating vector

z in anticlockwise direction through 90° . Therefore,OA ⊥ AB.So,

Area of ΔOAB = 1/2 OA x OB

= 1/2|z||iz| = 1/2 |z|2.

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