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Question

Let z1 ,z2 be two complex numbers such that z1+z2 and
z1z2 both are real , then

A
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B
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C
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Solution

The correct option is B



Lets z1=a+ib,z2=c+id, then
z1+z2 is real (a+b)+i(b+d) is real
b+d=0 d=b ..............(i)
z1 z2 is real (adbd)+i(ac+bc) is real
ad+dc=0 a(b)+bc=0 a=c
z1=a+ib=cid=(¯z2 ( a=c and b=d)


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