For a non-zero complex number z, let arg(z) denote the prin…

Maths Complex Number JEE (Advanced) / IIT - JEE Problems (Previous Years) More Than One Correct MCQ

Published on: August 14, 2026

For a non-zero complex number z, let arg(z) denote the principal argument with –π < arg(z) π. Then, which of the following statement(s) is (are)

Arg(–1 –i) =

, where i =

The function f : R → (–π, π], defined by f(t) = arg(–1 + it) for all t ∈ R, is continuous at all points of R, where i =

For any two non-zero complex numbers z 1 and z 2 ,

is an integer multiple of 2π

For any three given distinct complex numbers z 1 , z 2 and z 3 , the locus of the point z satisfying the condition arg

= π, lies on a straight line.

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a, b, d)

Sol. Arg (–1 –i) = –

f(t) = Arg(–1 + it)

It is discontinuous at t = 0

Arg – Arg z 1 + Argz 2

Arg = Arg z 1 – Arg z 2 + 2nπ

so the expression becomes 2nπ

Arg = π

It is circle

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