Question

Assertion :If $z_1\ne z_2$ and $|z_1+z_2|=|\frac{1}{z_1}+\frac{1}{z_2}|$ then

$z_1{z}_2$ is unimodular.

Reason: Both $z_1$ and $z_2$ are unimodular.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect and Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

$\left|z_1{+z}_2\right|=|\frac{1}{z_1}+\frac{1}{z_2}|$
$⟹\left|z_1{+z}_2\right|=\left|\frac{z_1+z_2}{z_1{z}_2}\right|$
$\because z_1\ne {-z}_2$
$\therefore \left|z_1{z}_2\right|=1$
Therefore $z_1{z}_2$ is unimodular.
But $z_1$ & $z_2$ are not unimodular.
Ans: c