The area of the triangle whose vertices are complex numbers z, i z, z+i z in the Argand diagram is

Step-by-step solution

Vertices of triangle in complex form is z, i z, z+i z In cartesian form vertices are (x, y),(-y, x) and (x-y, x+y) aligned & Area of triangle = 1 2 | array ccc x & y & 1 -y & x & 1 x-y & x+y & 1 array | & = 1 2 [x(x-x-y)-y(-y-x+y)+1 & . (-y x-y^2-x^2+x y ) ] aligned aligned & = 1 2 [-x y+x y-y^2-x^2 ]= 1 2 (x^2+y^2 ) & ( Area can not be negative ) & = 1 2 |z|^2 ( z=x+i y,|z|^2=x^2+y^2 ) aligned