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For two non-zero complex numbers z1 and z2, if Re(z1z2) = 0 and Re(z1 + z2), then which of the following are possible? A. Im(z1) > 0 and Im(z2) > 0 B. Im(z1) < 0 and Im(z2) > 0 C. Im(z1) > 0 and Im(z2) < 0 D. Im(z1) < 0 and Im(z2) < 0 Choose the correct answer from the options given below

1. B and C
2. B and D
3. A and B
4. A and C

Correct answer: B and C

Solution

The condition Re(z1z2) = 0 indicates that the product of the two complex numbers is purely imaginary, which occurs when one number has a positive imaginary part and the other has a negative imaginary part. Therefore, options B (Im(z1) < 0 and Im(z2) > 0) and C (Im(z1) > 0 and Im(z2) < 0) are valid scenarios that satisfy this condition.

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