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Show that the area of the triangle on th...

Show that the area of the triangle on the Argand diagram formed by the complex number `z ,i za n dz+i z` is `1/2|z|^2`

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We have `iz = z e^(i pi //2)` . This implies that iz is the vector obtained by rotating vector z in anti-clockwise direction through `90^(@)` . Therefore , `OA bot AB` . So

Area of `Delta OAB = (1)/(2) OA xx OB = (1)/(2) |z| |iz| = (1)/(2) |z|^(2)`
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