Question

If 0, 3 + 4i, 7 + 7i, 4 + 3i are vertices of a quadrilateral,then it is a

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

Answer 1

The correct option is D rhombus

$P,Q,R,S$ are represented by the complex numbers $0,3+4i,7+7i,4+3i$ are vertices of a quadrilateral respectively
$PQ=|3+4i|=5$,$QR=|4+3i|=5$,$RS=|-3-4i|=5$ and $SP=|-4-3i|=5$
$PR=|7+7i|=7\sqrt{2}$ and $QS=|1-i|=\sqrt{2}$
$\Rightarrow$ All sides are equal and Diagonals are not equal.
i.e $PQRS$ is a Rhombus.
Hence, option D.