Question

The figure formed by the points $(2+i),(4+3i),(2+5i),\left(3i\right)$ in argand plane is a

• A. circle
• B. square
• C. rectangle
• D. rhombus

Answer 1

The correct option is B square

Let the given points be $A:(2+i),B:(4+3i),C:(2+5i),D:\left(3i\right)$.

The plotting of these points in the complex plane is similar to the plotting on argand plane when the points are $A:(2,1),B:(4,3),C:(2,5),D:(0,3)$

The figure formed will be same in both the planes.

So, we check the figure in argand plane.

We find the distances $AB,AC,AD,BC,BD$ and $CD$

$AB=\sqrt{{(4-2)}^2+{(3-1)}^2}=2\sqrt{2}$ units

$AC=\sqrt{{(2-2)}^2+{(5-1)}^2}=4$ units

$AD=\sqrt{{(2-0)}^2+{(3-1)}^2}=2\sqrt{2}$ units

$BC=\sqrt{{(4-2)}^2+{(3-5)}^2}=2\sqrt{2}$ units

$BD=\sqrt{{(4-0)}^2+{(3-3)}^2}=4$ units

$CD=\sqrt{{(2-0)}^2+{(3-1)}^2}=2\sqrt{2}$ units

From these lengths of the figure, it can be noted that $4$ sides are equal and two diagonals are equal.

So, the given figure is a square.