Chapter 1: Complex Numbers- MCQs | National Book Foundation

Chapter 1: Complex Numbers-MCQs Preparation Test| National Book Foundation

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Chapter 1: Complex Numbers | National Foundation Book

June 20, 2025

Name

Class

In a complex plane imaginary part is drawn along _______

xy-plane

x-axis

origin

y-axis

None

One factor of $2z^2 +18$ is

$z-3i$

$z-4i$

$z-5i$

$z-2i$

None

$i^{14}=?$

$1$

$-1$

$i$

$-i$

None

Multiplicative identity of complex number is;

$(1,0)$

$(0,-1)$

$(0,0)$

$(1,1)$

None

$(\cos {\frac{\pi}{6}}+i\sin{\frac{\pi}{6}})^6$ is equal to ________

$i$

$0$

$-1$

$1$

None

The multiplicative inverse of complex number $(a,b)$ is

$(\frac{a}{a^2 +b^2} ,\frac{-b}{a^2 +b^2})$

$(\frac{-a}{a^2 +b^2} ,\frac{b}{a^2 +b^2})$

$(\frac{a}{a^2 +b^2} ,\frac{b}{a^2 +b^2})$

$(\frac{-a}{a^2 +b^2} ,\frac{-b}{a^2 +b^2})$

None

The value of $(\sqrt{-25})(\sqrt{-4})$ is

$10i$

$-10$

$-10i$

None

The real part of complex number $(\cos {\theta}+i\sin{\theta})^n$ where $n \in Z$ will be

$\cos^n {\theta}$

$\cos {n\theta}$

$\sin {n\theta}$

$\sin^n {\theta}$

None

Polar form of complex number $r\cos {\theta}+ir\sin{\theta}$ then $\theta=?$

$\tan {\frac{x}{y}}$

$\tan^{-1} {\frac{x}{y}}$

$\tan^{-1} {\frac{y}{x}}$

$\tan{\frac{y}{x}}$

None

10.

Real part of $\frac{3}{\sqrt{6} -\sqrt{-12}}$ is;

$\frac{1}{\sqrt{6}}$

$\sqrt{6}$

None of these

$\frac{3}{\sqrt{6}}$

None

11.

If $(\frac{1+i}{1-i})^n =1$ then least positive value of $n$ is

None

12.

If $z=a+bi$ what is the value of $\cos {\theta}$?

$\frac{b}{a}$

$\frac{b}{|z|}$

$\frac{a}{|z|}$

$\frac{a}{b}$

None

13.

Conjugate of complex number $-2+3i$ is ______

$-2-3i$

$2+3i$

$-2+3i$

$2-3i$

None

14.

Every complex number has _______ part(s).

one

two

three

None

15.

If $z=3+4i$ then $z^{-1}$ is

$(\frac{3}{25} , \frac{-4}{25})$

$(\frac{3}{25} , \frac{4}{25})$

$(\frac{-1}{3} , \frac{-1}{4})$

$(\frac{1}{3} , \frac{1}{4})$

None

16.

The multiplicative inverse of complex number $(0,-1)$ is

$(1,0)$

$(0,1)$

$(-1,0)$

$(0,0)$

None

17.

$(-i)^{-7}=?$

$-i$

$1$

$i$

$-1$

None

18.

Modulus of complex number $a+bi=?$

$a^2 +b^2$

$\sqrt{a^2 +b^2}$

$a^2-b^2$

$\sqrt{a^2-b^2}$

None

19.

if $z_1$ $= 3+2i$ and $z_2$ $=5+6i$ then

$z_1$ $>$$z_2$

$\overline{z_1} = \overline{z_2}$

$z_1$ $<$ $z_2$

$\overline{z_1} = -\overline{z_2}$

None

20.

If $z$ is a complex number then its mirror image is __________

$\frac{1}{z}$

$-z$

$\overline{z}$

$|z|$

None

21.

The equation $x^2 +1 =0$ has solution in

$\mathbb{R}$

$\mathbb{C}$

None

22.

$z \in \mathbb{C}, \quad z + \overline{z}$ is ________

real number

complex number

rational number

irrational number

None

23.

If $z_1 = 1 + i, \quad z_2 = 1 - i$ then

$z_1 > z_2$

$\overline{z_1}>\overline{z_2}$

$z_1 < z_2$

$|z_1|=|z_2|$

None

24.

Additive inverse of $(a,b)$ in $\mathbb{C}$ is

$(a,-b)$

$(-a,-b)$

$(a,b)$

$(-a,b)$

None

25.

The $\sqrt{-1}$ is called

natural number

rational number

real number

complex number

None

26.

Every real number is also a _______ number

integer

natural

rational

complex

None

27.

$(-1)^{\frac{-21}{2}}=?$

$-i$

$i$

$1$

$-1$

None

28.

Diagram representing a complex number is called _____ diagram.

Venn

argand

ordered pair

vector

None

29.

Magnitude of complex number $z$ is the distance of z from _______.

(1,1)

(0,1)

(1,0)

(0,0)

None

Chapter 1: Complex Numbers-MCQs Preparation Test| National Book Foundation

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