Complex Numbers
Modulus and Properties
Premium Question
Grade 11
Question:
If $w = \frac{z - 1}{z + 1}$ is purely imaginary, then $|z|$ equals:
(1) $2$
(2) $1$
(3) $\sqrt{2}$
(4) $3$
Step-by-Step Solution
Key Concept: Write $z = x + iy$. Expand $w$ by multiplying by the conjugate denominator. The real part of $w$ involves only $x$ and $|z|^2$. Set it to zero.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)