Let z=x+iy ⇒ |z|=√x2+y2⇒iz=ix+i2y=ix−y ⇒ |iz|=√x2+y2 ⇒ z+iz=(x+iy)+(ix−y)=(x−y)+i(x+y) ⇒ |z+iz|=√(x−y)2+(x+y)2 = √2x2+2y2 ∴ The triangle formed by the sides |z|,|iz| and |z+iz| is an isosceles right angled triangle with hypotenuse |z+iz|. Area of triangle =