If $|u| < 1,|v| < 1$ and $z=\frac{u-v}{1-u v}$, a lower bound of $|z|$ is

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

|u| < 1,|v| < 1

and

z=\frac{u-v}{1-u v}

, a lower bound of

|z|

View answer and explanation

Correct option: C

\frac{\|u|-| v\|}{1+|u||v|}

Option C (

\frac{{\|u|-|v\|}}{{1+|u||v|}}

) is correct because by using properties of complex numbers and the reverse triangle inequality, we can establish the lower bound for |z|.

Practice All Chapter MCQs →

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