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Q.

For two non-zero complex number z1 and z2, if Re (z1z2)=0 and  Re (z1+z2)=0 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:

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a

B and D

b

A and B

c

A and C

d

B and C

answer is A.

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Detailed Solution

detailed_solution_thumbnail

Let z1=x1+iy1,z2=n2+iy2
x1+x2=0⇒x2=−x1x1x2−y1y2=0y1y2=−x12<0∴y1,y2 have opp. signs 

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