All the points in the set S = α + i α - i , α ∈ R , i = - 1 lie on a

Given z = α + i α - i , since α ∈ R ⇒ z = α + i α - i = α + i α - i ⇒ z = α 2 + 1 2 α 2 + - 1 2 ⇒ z = 1 Hence, locus of z is a circle with radius 1 .

Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeometric ApplicationEasy2 minPYQ_2019

MathematicsEasysingle choice

All the points in the set $S = \{\frac{α + i}{α - i}, α \in R\}, i = \sqrt{- 1}$ lie on a

Answer:

Solution:

Given $z = \frac{α + i}{α - i}$ , since $α \in R$

$\Rightarrow |z| = |\frac{α + i}{α - i}| = \frac{|α + i|}{|α - i|}$

$\Rightarrow |z| = \frac{\sqrt{α^{2} + 1^{2}}}{\sqrt{α^{2} + {(- 1)}^{2}}}$

$\Rightarrow |z| = 1$

Hence, locus of $z$ is a circle with radius $1$ .

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Geometric Application

⏱ 2mℹ️ Source: PYQ_2019

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