If z, bar{z}, -z, -bar{z} form a rectangle of | vedclass

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(A) Let $z = x + iy$. Then,the vertices of the rectangle in the Argand plane are $(x, y), (x, -y), (-x, -y),$ and $(-x, y)$. The length of the sides o

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$\frac{1}{2}+\sqrt{3} i$

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(A) Let $z = x + iy$. Then,the vertices of the rectangle in the Argand plane are $(x, y), (x, -y), (-x, -y),$ and $(-x, y)$. The length of the sides of the rectangle are $|x - (-x)| = |2x|$ and $|y - (-y)| = |2y|$. Since $x$ and $y$ are coordinates,the side lengths are $2|x|$ and $2|y|$. The area of the rectangle is $(2|x|)(2|y|) = 4|xy|$. Given that the area is $2\sqrt{3}$,we have $4|xy| = 2\sqrt{3}$,which implies $|xy| = \frac{\sqrt{3}}{2}$. For option $A$,$z = \frac{1}{2} + \sqrt{3}i$,so $x = \frac{1}{2}$ and $y = \sqrt{3}$. Then $|xy| = |\frac{1}{2} 	imes \sqrt{3}| = \frac{\sqrt{3}}{2}$. Thus,$z = \frac{1}{2} + \sqrt{3}i$ is a valid solution.

If $z, \bar{z}, -z, -\bar{z}$ form a rectangle of area $2 \sqrt{3}$ square units,then one such $z$ is

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