If z5 = (z – 1)5, then the roots are represented in the argand plane by the points that are

To solve the equation z5 = (z – 1)5, we can start by expanding both sides using the binomial theorem.

On the left side, we have z5 = z * z * z * z * z.

On the right side, we have (z – 1)5 = (z – 1) * (z – 1) * (z – 1) * (z – 1) * (z – 1).

Expanding both sides further, we get:

z5 = z * z * z * z * z (z – 1)5 = (z – 1) * (z – 1) * (z – 1) * (z – 1) * (z – 1)

Now, we can equate the corresponding terms on both sides:

z = z – 1 z = z – 1 z = z – 1 z = z – 1 z = z – 1

Simplifying each equation, we find that z = 1.

Therefore, the equation z5 = (z – 1)5 has only one root, which is z = 1.

In the Argand plane, this root is represented by the point (1, 0), which lies on the real axis.