Question

Show that the points in the Argand plane represented by the complex numbers $-2+7i,\frac{-3}{2}+\frac{1}{2}i,4-3i,\frac{7}{2}(1+i)$ are the vertices of a rhombus.

Answer 1

Let the point $(-2+7i)$ be $A$ , $(\frac{-3}{2}+\frac{1}{2}i)$ be $B$ , $(4-3i)$ be $C$ and $\left(\frac{7}{2}\right(1+i\left)\right)$ be $D$

Observe that $AB=BC=CD=\frac{\sqrt{170}}{2}$

All sides are equal, therefore the points are the vertices of rhombus