Area of triangle on the argand plane formed by complex numbers z,iz,z+iz is
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Complex numbers forming the triangle = z, iz, z + iz
Since, Z and iZ are perpendicular to each other.
then the complex number will be multiplied by i and the new complex number will also be perpendicular to each other.
Hence the given three numbers z, iz, z + iz will form a right angled triangle.
Therefore, the area will be
= 1/2 × |z| × |iz|
= 1/2 |z|²
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