Question

If z⁴ = (z – 1)⁴, than the roots are represented in complex plane by the points that are

• A. Collinear
• B. Concylic
• C. Vertices of a parallelogram
• D. None of these

Answer 1

Answer: (A)

Collinear

Answer 2

Sol. $z^{4} = (z - 1)^{4} \Rightarrow \left( \frac{z}{z - 1} \right)^{4} = 1$

Ž $\frac{z}{z - 1} = (1)^{1/4}$ Ž $\left| \frac{z}{z - 1} \right| = 1$ Ž |z| = |z–1|

So they lie on the line bisecting perpendicularly the join of z = 1 & z = 0