The points $9 + i, 4 + 13 i, - 8 + 8 i, - 3 - 4 i$ in the Argand diagram represent a :

Rhombus

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Square

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Rectangle

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Parallelogram

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Solution

The correct option is D Square
The points can be re-written as
$(9, 1), (4, 13), (- 8, 8), (- 3, - 4)$
Let
$A = (9, 1)$
$B = (4, 13)$
$C = (- 8, 8)$
$D = (- 3, - 4)$
Hence,
$A B = 13$
$B C = 13$
$C D = 13$
$A D = 13$
Hence,
The geometrical figure formed by the points is rhombus.
Let
$Z_{1} = A B = 5 - 12 i$
$Z_{2} = B C = 12 + 5 i$
Hence, the angle between $z_{1}$ and $z_{2}$ is $\frac{π}{2}$ .
Thus, the adjacent sides are perpendicular.
Hence, the shape is a square.

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The points 9+i,4+13i,−8+8i,−3−4i in the Argand diagram represent a :

The points $9 + i, 4 + 13 i, - 8 + 8 i, - 3 - 4 i$ in the Argand diagram represent a :