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Complex Numbers question

2023 · 29 Jan · Shift 1 · Q31

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2023 · 29 Jan · Shift 1 · Q31

Complex Numbers question

2023 · 29 Jan · Shift 1 · Q31

JEE MainMathematicsComplex NumbersMCQ+4 / −1

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)=0

, then which of the following are possible? A.

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

and

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

B.

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

C.

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

and

\operatorname{Im}\left(z_{2}\right) D.

\operatorname{Im}\left(z_{1}\right) Choose the correct answer from the options given below :

A
A and C
B
A and B
C
B and D
D
B and C

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