Question

If `"z"^2/(("z" - 1))` is always real, then z, can lie on ______.

Options

• real axis

• a parabola

• imaginary axis

• pair of lines

Answer 1

If `z^2/((z - 1))` is always real, then z, can lie on real axis.

Explanation:

∵ `(x + "iy")^2/((x - 1 + "iy")) xx (((x - 1) - "iy"))/(((x - 1) - "iy"))` = `((x^2 - "y"^2 + 2"i"x"y")[(x - 1) - "iy"])/((x - 1)^2 + "y"^2)`

Always real so

2xy(x – 1) – y(x² – y²) = 0

⇒ y(2x² – 2x – x² + y²) = 0

⇒ y(x² – 2x + y²)= 0

⇒ y = 0 real axis