For two non-zero complex numbers $ z_{1} $ and $ z_{2} $, if $ \operatorname{Re}\left(z_{1} z_{2}\right)=0 $ and $ \operatorname{Re}\left(z_{1}+z_{2}\right) $, then which of the following are possible? A. $ \operatorname{Im}\left(z_{1}\right)>0 $ and $ \operatorname{Im}\left(z_{2}\right)>0 $ B. $ \operatorname{Im}\left(z_{1}\right) 0 $ C. $ \operatorname{Im}\left(z_{1}\right)>0 $ and $ \operatorname{Im}\left(z_{2}\right)<0 $ D. $ \operatorname{Im}\left(z_{1}\right)<0 $ and $ \operatorname{Im}\left(z_{2}\right)<0 $ Choose the correct answer from the options given below

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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For two non-zero complex numbers

z_{1}

and

z_{2}

, if

\operatorname{Re}\left(z_{1} z_{2}\right)=0

and

\operatorname{Re}\left(z_{1}+z_{2}\right)

, then which of the following are possible?
A.

\operatorname{Im}\left(z_{1}\right)>0

and

\operatorname{Im}\left(z_{2}\right)>0

\operatorname{Im}\left(z_{1}\right)<0

and

\operatorname{Im}\left(z_{2}\right)>0

\operatorname{Im}\left(z_{1}\right)>0

and

\operatorname{Im}\left(z_{2}\right)<0

\operatorname{Im}\left(z_{1}\right)<0

and

\operatorname{Im}\left(z_{2}\right)<0

Choose the correct answer from the options given below

View answer and explanation

Correct option: A

B and C

Options B and C are correct because they represent the possible scenarios where the product of the imaginary parts of the two complex numbers is negative, satisfying the given conditions.

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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