1. Tardigrade
  2. Question
  3. Mathematics
  4. The points 0, 2 + 3i, i, - 2 - 2i in the argand plane are the vertices of a

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The points $ 0, 2 + 3i, i, - 2 - 2i $ in the argand plane are the vertices of a

Complex Numbers and Quadratic Equations

Solution:

Let $A = 0$,
$B = 2 + 3i$,
$C = i$,
$D = - 2 - 2i$
Now, $AB=\sqrt{2^{2}+3^{2}}=\sqrt{13}$
$BC=\sqrt{2^{2}+2^{2}}=\sqrt{8}$
$CD=\sqrt{2^{2}+3^{2}}=\sqrt{13}$
$DA=\sqrt{2^{2}+2^{2}}=\sqrt{8}$
Diagonals $AC=\sqrt{0+1^{2}}=1$
and $BD=\sqrt{\left(4\right)^{2}+\left(5\right)^{2}}=\sqrt{41}$ which are not equal.
Hence given vertices are the vertices of a parallelogram.