Area of a triangle with complex coordinates

If \[p(z_1)\] ,\[q(z_2)\] and \[r(z_2)\] are the coordinates of the triangle then area of triangle is given by\[ \begin{vmatrix} z_1& \bar{z_1} & 1 \\ z_2 & \bar{z_2} & 1 \\ z_3& \bar{z_3} & 1 \\ \end{vmatrix}\]

where \[ z_1=a+ib\]  \[ \bar{z_1}=a-ib\]\[ \]

             \[ z_2=c+id\] \[ \bar{z_2}=c-id\]

          \[ z_3=p+iq\]   \[ \bar{z_3}=p-iq\]

Posted on by