JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

If for the complex numbers

z_1

and

z_2

\left|1-\bar{z}_1 z_2\right|^2-\left|z_1-z_2\right|^2=k\left(1-\left|z_1\right|^2\right)\left(1-\left|z_2\right|^2\right)

, then

k

is equal to

View answer and explanation

Correct option: A

Option A (1) is correct because by expanding and simplifying the given expression, it reduces to

(1-|z_1|^2)(1-|z_2|^2)

, which implies

k=1

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