Question
Question: If the roots of (z – 1)<sup>n</sup> = i (z + 1)<sup>n</sup> are plotted in the argand plane, they ar...
If the roots of (z – 1)n = i (z + 1)n are plotted in the argand plane, they are-
A
On a parabola
B
Concyclic
C
Collinear
D
The vertices of a triangle
Answer
Collinear
Explanation
Solution
Sol. We have (z – 1)n = i (z + 1)n
\ |z – 1|n = |i| |z + 1|n
Ž |z – 1|n = |z + 1|n
Ž |z – 1| = |z + 1|
Ž |z – 1|2 = |z + 1|2
Ž (x – 1)2 + y2 = (x + 1)2 + y2
\ 4x = 0 Ž x = 0.
\ The roots lies on the y-axis.