Home > Complex Numbers > jee_adv_2026_mock_p2 > f59b591c-1c3f-4ec5-a55e-016c4bd767e5

Not the exact question you were looking for?

Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.

Complex Numbers

Geometry of Complex Numbers

jee_adv_2026_mock_p2

Grade 12

Question:

If |z| = 1, then the number of possible values of z is:

A. 0

B. 1

C. 2

D. 4

Step-by-Step Solution

Key Concept: Intersection of y = x and |z| = 1.

Step 1: z lies on y = x and |z| = 1. Step 2: z = x + ix, |z| = √(x^2 + x^2) = √2|x| = 1 => x = ±1/√2. Step 3: z = (1/√2)(1 + i) or (-1/√2)(1 + i). Two values.

Correct Answer: C

Mathbee AI Mentor (Free Demo)

Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.