Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeometric ApplicationMedium2 minPYQ_2024

MathematicsMediumsingle choice

If $z, \overset{z}{ˉ}, - z, - \overset{z}{ˉ}$ forms a rectangle of area $23$ square units, then one such $z$ is

Question diagram: If z , z ˉ , − z , − z ˉ forms a rectangle of area 2 3 squ

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Solution:

Let a complex number, $z = x + i y$ $\Rightarrow \overset{z}{ˉ} = \overset{x}{ˉ} - i y$ Then, vertices of rectangle for $z, \overset{z}{ˉ}, - z, - \overset{z}{ˉ}$ are $(x, y), (x, - y), (- x, - y), (- x, y)$ Now, Area of rectangle $= (2 x) (2 y) = 4 x y$ It is given that, Area $= 23 = 4 x y \Rightarrow 2 x y = 3$ $∴ x = \frac{1}{2}, y = 3 ∴ z = \frac{1}{2} + 3 i$

Subject:MathematicsTopic:Complex NumberSubtopic:Geometric Application

⏱ 2mℹ️ Source: PYQ_2024

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