Question

The area of the triangle formed by the complex numbers $2+3i,1+i,i-1$ in square units is:

• A. $\frac{1}{2}$
• B. $1$
• C. $\sqrt{2}$
• D. $2$

Answer 1

The correct option is D $2$

The points on the Argand Plane are $(2,3)$, $(1,1)$ and $(-1,1)$.

$\text{Area}=\frac{1}{2}\left|\begin{array}{cc}1& 11\\ 2& 1-1\\ 3& 11\end{array}\right|=\frac{1}{2}\left|\left(1\right(1+1)-1(2+3)+1(2-3\left)\right)\right|$

$=2$