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Question

A triangle is formed on the Argand plane by the complex numbers z,iz and z+iz. If |z|=2, then area of triangle is sq. unit

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Solution


Let the vertices of the triangle be A(z),B(iz),C(z+iz).
We know that iz is obtained by rotating OA through an angle 90.
From the diagram, OA=OB=BC=AC,O=90
Hence OABC will be a square

From Argand diagram, it is clear that
Area of ABC = Area of OAB
=12×OA×(OB) [it is right angled at point O]
=12|z|×|iz|
=12|z|2=2 sq. unit

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