Question

Let \( z \neq 1 \) be a complex number and let \( \omega = x + iy, y \neq 0 \). If \[ \frac{\omega -\overline{\omega}z}{1 -z} \] is purely real, then \( |z| \) is equal to

• A. \( |\omega| \)
• B. \( |\omega|^2 \)
• C. \( \frac{1}{|\omega|^2} \)
• D. 1

Hint:

For a complex number to be purely real, its imaginary part must be zero. This condition can be used to solve for unknown variables in complex expressions.