Question

The area of the triangle formed by $1+i,i-1$ and $2i$ in the Argand plane is

• A. $3\text{sq. units}$
• B. $4\text{sq. units}$
• C. $1\text{sq. units}$
• D. $2\text{sq. units}$

Answer 1

The correct option is C $1\text{sq. units}$

Let
$z_1=1+i\Rightarrow (x_1,y_1)=(1,1)z_2=-1+i\Rightarrow (x_2,y_2)=(-1,1)z_3=2i\Rightarrow (x_3,y_3)=(0,2)$

Area of triangle
$△=\frac{1}{2}\left|\begin{array}{cc}{x}_1& y_1\\ x_2& y_2\\ x_3& y_3\\ x_1& y_1\end{array}\right|$

$\Rightarrow △=\frac{1}{2}\left|\begin{array}{cc}1& 1\\ -1& 1\\ 0& 2\\ 1& 1\end{array}\right|\Rightarrow △=\left|\frac{1}{2}\left[\right(1+1)+(-2-0)+(0-2\left)\right]\right|\therefore △=1\text{sq. units}$