Complex Numbers - HSSC-I Mathematics

5 practice questions for this chapter, gradeable instantly.

ClassSubjectChapterTopicSLODifficultyPast paperSort

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

AKU-EB Model Paper 2025EASY

$(2+2i)(2-2i)$ 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

AKU-EB Model Paper 2025MEDIUM

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

AKU-EB Model Paper 2025MEDIUM

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

AKU-EB Model Paper 2025EASY

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

AKU-EB Model Paper 2025HARD

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