Questions
If and are two complex numbers such that , then
a
z2=kz1,k∈R
b
z2=ikz1,k∈R
c
z1=z2
d
none of these
detailed solution
Correct option is B
Note that at least one of z1,z2 is different from 0. Suppose z2≠0 we can writez1−z2z1+z2=1, as z1/z2−1z1/z2+1=1 or as z1z2−1=z1z2+1This shows that z1/z2 lies on the perpendicular bisector of the segment joiningA(−1+i0) andB(1+i0) [See Theory].Thus, z1/z2 lies on the imaginary axis.∴ z1z2=ia for some a∈R. ⇒z2z1=1ia=−ia⇒ z2=ikz1 for some k∈RTalk to our academic expert!
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