NTA Abhyas JEE Main2020MathematicsComplex NumberPractice

For a complex number Z , the equation of the line of common chord of the circles Z - 3 = 2 and Z = 2 is

Options

AZ + Z ¯ = 3
BZ - Z ¯ = 3
CZ ¯ - Z = 3
DZ + Z ¯ + 3 = 0

Correct answer

A. Z + Z ¯ = 3

Step-by-step solution

Z - 3 = 2 ⇒ Z - 3 Z ¯ - 3 ¯ = 4 ⇒ Z Z ¯ - 3 Z - 3 Z ¯ + 9 = 4 … 1 Z = 2 ⇒ Z Z ¯ = 4 … 2 For the equation of common chord, Subtracting 2 from 1 , we get, - 3 Z - 3 Z ¯ + 9 = 0 ⇒ Z + Z ¯ = 3

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