Welcome to the NDA 1 2024 Maths Lecture on Complex Numbers and Multiple Choice Questions (MCQs). Today, we’ll embark on a journey into complex numbers, exploring various concepts and tackling MCQs to enhance our understanding. Whether you’re preparing for an exam or simply refreshing your knowledge, this lecture aims to equip you with the skills needed to master complex numbers.

NDA 1 2024 Complex Numbers MCQs Maths Lecture

Understanding Complex Numbers

Let’s begin by understanding what complex numbers are. A complex number consists of a real part and an imaginary part, typically denoted as a + bi, where ‘a’ represents the real part, ‘b’ represents the imaginary part, and ‘i’ represents the imaginary unit (√-1). Complex numbers are powerful mathematical tools in various fields, including engineering, physics, and computer science.

Q) sin x + i cos 2x and cos x – i sin 2x are conjugate to each other for

A. x = nπ

B. x = (n + ½) π/2

C. x = 0

D. No value of x

Ans : D

Q) If the complex number z = x + iy satisfies the condition | z + 1 |= 1, then z lies on

A. x-axis

B. circle with centre (1, 0) and radius 1

C. circle with centre (–1, 0) and radius 1

D. y-axis

Ans : C

Q) If ω denotes the cube root of unity, then what is the real root of the equation ?

A. 3ω

B. 3ω²

C. −3ω

D. 3ω³

Ans : D

Q) The point represented by the complex number 2 – i is rotated about origin through an angle π/2 in the clockwise direction, the new position of point is

A. 1 + 2i

B. −1 − 2i

C. 2 + i

D. −1 + 2i

Ans : B

Q) The square root of 3 − 4i  is

A. ± ( 2 − i)

B. ± 3i

C. ± (3 − i)

D. ± − (4 − I)

Ans : A

For an explanation of the above questions and other related MCQs, please refer to the YouTube video above.