Complex Numbers
Complex Numbers
nta_abhyas_2025
Grade 11
Question:
A complex number $z$ is said to be unimodular if $|z| = 1$. Let $z_1$ and $z_2$ are complex numbers such that $\frac{z_2 - z_1}{z_2 - z_3}$ is unimodular and $z_2$ is not real. Then $z_1$ lies on a
circle of radius √2
straight line parallel to x-axis
straight line parallel to y-axis
circle of radius 2
Step-by-Step Solution
Key Concept: The modulus of a product of complex numbers equals the product of their moduli.
We are given $|c| = 1$ and $|x| = 1$ and $|y| = 1$. From the condition $|c| = 1 \times 1 \times 1$, we get $|c| = 1$.
Correct Answer: 1