If Z -lies on the circle ∣ z − 2 i ∣ = 2 2 then value of ar g ( Z + 2 Z − 2 ) is

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MathematicsComplex NumberGeometric ApplicationMedium2 min

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If $Z$ -lies on the circle $∣ z - 2 i ∣ = 22$ then value of $ar g (\frac{Z - 2}{Z + 2})$ is

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Solution:

Circle with centre $(0, 2)$ cuts $X$ -axis at $A (- 2, 0)$ and $B (2, 0)$ . Now $A B$ subtends an angle $9 0^{0}$ at the center $C$ . AB subtends an angle $\frac{π}{4}$ at any point $z$ on the major arc circle arg $(\frac{z - 2}{z + 2}) = \frac{π}{4}$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Geometric Application

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