Question

If P, Q, R, S are represented by the complexnumbers $-4+i,$ $-1+6i,4+3i,$ $1-2i$ respectively,then PQRS is a

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

Answer 1

Answer: (B)

square

$P,Q,R,S$ are represented by the complex numbers $-4+i,-1+6i,4+3i,1-2i$ respectively

$\Rightarrow PQ=|3+5i|=\sqrt{34}$,$QR=|5-3i|=\sqrt{34}$,$RS=|-3-5i|=\sqrt{34}$ and $SP=|-5+3i|=\sqrt{34}$

$\Rightarrow PR=|8+2i|=\sqrt{68}$ and $QS=|2-8i|=\sqrt{68}$

$\Rightarrow$ All sides are equal and Diagonals are equal.

i.e $PQRS$ is a square.
Hence, option B.