If z_1 and z_2 are two non-zero complex numbers such that |z_1 + z_2| = |z_1| + |z_2| , then z_1 - z_2 is equal to: - Mathematics MCQ AIEEE 2026 | ExamTest.live

mediumMCQAIEEE2026Mathematics

1 mark

If z_{1} and z_{2} are two non-zero complex numbers such that ∣ z_{1} + z_{2} ∣ = ∣ z_{1} ∣ + ∣ z_{2} ∣, then ar g z_{1} - ar g z_{2} is equal to:

Solution & Step-by-step Explanation

Let z_{1} = r_{1} e^{i θ_{1}} and z_{2} = r_{2} e^{i θ_{2}} . ∣ z_{1} + z_{2} ∣^{2} = (∣ z_{1} ∣ + ∣ z_{2} ∣)^{2} ∣ z_{1} ∣^{2} + ∣ z_{2} ∣^{2} + 2∣ z_{1} ∣∣ z_{2} ∣ cos (θ_{1} - θ_{2}) = ∣ z_{1} ∣^{2} + ∣ z_{2} ∣^{2} + 2∣ z_{1} ∣∣ z_{2} ∣ 2∣ z_{1} ∣∣ z_{2} ∣ cos (θ_{1} - θ_{2}) = 2∣ z_{1} ∣∣ z_{2} ∣ Since z_{1}, z_{2} \neq = 0 : cos (θ_{1} - θ_{2}) = 1 θ_{1} - θ_{2} = 0 Thus, ar g z_{1} - ar g z_{2} = 0 .

Try it yourself before checking the explanation above.

If z_{1} and z_{2} are two non-zero complex numbers such that ∣ z_{1} + z_{2} ∣ = ∣ z_{1} ∣ + ∣ z_{2} ∣, then ar g z_{1} - ar g z_{2} is equal to:

π /2

- π

0

- π /2

Practice with timed mock tests and track your performance across Mathematics.