Questions
If and then all the values of lie on:
a
a line not passing through the origin.
b
z=2
c
the x-axis
d
the y- axis
detailed solution
Correct option is D
As z=1, we get zz¯=1.Let w=z1-z2, thenw+w¯=z1−z2+z¯1−z¯2=z1−z2+1/z1−(1/z)2 =z1−z2+zz2−1=0⇒ 2Re(w)=0 ⇒ Re(w)=0Thus, w lies on the y- axis.Alternate Solutionw=z1−z2=zzz¯−z2=1z¯−z=1−2iIm(z)⇒ w is purely imaginary, that is, w lies on the y-axis.Talk to our academic expert!
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