AKUEB Class 11 (HSSC-I) Mathematics Complex Numbers MCQs & Practice Questions

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.1 Complex Numbers / 1.1.6

Past Paper 2024EASY

If $Z = 3 + i$ , then $\overline{\overline{Z}}$ will be

3-i

3+i

-3+i

-3-i

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.1 Complex Numbers / 1.1.5

Past Paper 2024EASY

The multiplicative inverse of $-2i$ is

\dfrac{2}{i}

\dfrac{-2}{i}

\dfrac{i}{2}

\dfrac{-i}{2}

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.1 Complex Numbers / 1.1.7

Past Paper 2024EASY

If the modulus of a complex number $(1, b)$ is $2$ , then $b$ is equal to

\pm 1

\pm 3

\pm\sqrt{5}

\pm\sqrt{3}

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.1 Complex Numbers / 1.1.5

Past Paper 2024EASY

On simplification of $3i^3 + 4i + 5$ , we get

5+i

5-i

2+4i

5-7i

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.3 Factorisation and Solution of Equations / 1.3.1

Past Paper 2025MEDIUM

The expression $x^4 + y^4$ can be factorised as

(x^2+iy^2)(x^2+iy^2)

(x^2-iy^2)^2 + 2ix^2y^2

(x^2-iy^2)(x^2+iy^2)

(x^2+iy^2)^2 - 2ix^2y^2

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.1 Complex Numbers / 1.1.7

Past Paper 2025MEDIUM

If $z = a - ib$ , then which one of the following options is false?

|z| = |-z|

|z| = |\bar{z}|

|z| = -|\bar{z}|

|z| = |-\bar{z}|

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.1 Complex Numbers / 1.1.7

Past Paper 2025EASY

If $Z = a - ib$ and $|Z| = 2$ , then the relationship between $a$ and $b$ is

a^2 - b^2 = 4

a^2 + b^2 = 4

a + b = 2

a - b = 2

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.1 Complex Numbers / 1.1.5

Past Paper 2025EASY

The simplified form of $2i \div (1+i)$ is equal to

1+i

1-i

2+2i

2-2i

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.1 Complex Numbers / 1.1.5

Model Paper 2026EASY

$(2+2i)(2-2i)$ is equal to

4

8

4-4i

8-8i

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.4 Complex Numbers in Polar Coordinates / 1.4.3

Model Paper 2026MEDIUM

Q10

In polar form, the complex number $z=3+4i$ can be represented as

z=5\left(\cos\dfrac{\pi}{4}+i\sin\dfrac{\pi}{4}\right)

z=5\left(\cos\dfrac{\pi}{3}+i\sin\dfrac{\pi}{3}\right)

z=5(\cos 53.13+i\sin 53.13)

z=5(\cos 0.927+i\sin 0.927)

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.3 Factorisation and Solution of Equations / 1.3.1

Model Paper 2026MEDIUM

Q11

The factorised form of the expression $x^4+y^4$ is

\left(x^2+iy^2\right)\left(x^2+iy^2\right)

\left(x^2-iy^2\right)^2+2ix^2y^2

\left(x^2-iy^2\right)\left(x^2+iy^2\right)

\left(x^2+iy^2\right)^2-2ix^2y^2

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.1 Complex Numbers / 1.1.6

Model Paper 2026EASY

Q12

The complex conjugate of $\left(2-i^2\right)^2$ is

-9

-6

3

9

Class 11 - Mathematics / Unit 1 - Complex Numbers / 1.3 Factorisation and Solution of Equations / 1.3.2

Model Paper 2026HARD

Q13

Fill the blank with the correct answer:

For the simultaneous linear equations with complex coefficients

ix - \sqrt{-4}\,y = \dfrac{8}{i} \qquad \text{and} \qquad \dfrac{x}{i} - iy = i^3

show that the value of

y

is real. The value of

y

Complex Numbers - Class 11 (HSSC-I) Mathematics