If z=x+iy , then area of the triangle whose vertices are points z,z+iz  and iz is:

Let z=x+iy;z+iz=(x−y)+i(x+y)  and iz=−y+ix If A  denotes the area of the triangle formed by z,z+izand iz , then A=12|xy1x−yx+y1−yx1|applying R2→R2−(R1+R3) , we getA=12|xy100−1−yx0|=12(x2+y2)=12|z|2 .