The area of the triangle on the argand plane formed by the complex numbers −z,iz,z−iz , is (where i=−1 ):

Let z=x+iy , then coordinates in ordered pair of the points corresponding the complex numbers −z , is and z−iz  are (−x,−y),(−y,x)  and (x+y,y−x) , respectively.Hence area of triangle =12|−x−y1−yx1x+yy−x1|=12|−x−y1−yx1003| (R2→R3+(R1+R2))Expand w.r.t. R3=32|−x−y−yx|=32(x2+y2)=32|z|2