Factorize z²+289:
- (z+17)(z−17)
- (z+17i)(z+17i)
- (z+17i)(z−17i)
- (z−17i)(z−17i)
Show answer and explanation
Answer: C. (z+17i)(z−17i)
289=17²; z²+17²=(z+17i)(z−17i).
FSC Mathematics: Number Systems, questions with answers
Practise 17 real Federal Board questions on Number Systems from 2023 to 2026. See the answer and explanation as soon as you answer.
17real questions
10multiple choice
5exam sessions
About Number Systems in FSC Mathematics
Number Systems is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (11th class), and about 4% of its real questions come from it. Tayyari Karo has 17 real questions on this chapter from 2023 to 2026; 10 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 8 medium, 7 easy, 2 hard.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
Argument of z=√3+i is:
- π/3
- π/4
- π/9
- π/6
Show answer and explanation
Answer: D. π/6
tanθ=1/√3 ⇒ θ=π/6.
The principal argument (θ) of the complex number z=−1+i√3 is:
- −π/3
- π/3
- 2π/3
- 5π/3
Show answer and explanation
Answer: C. 2π/3
|z|=2, z lies in 2nd quadrant, reference angle π/3 ⇒ θ=π−π/3=2π/3.
If z=x+iy, then in polar form z=r(cosθ+isinθ), where r equals:
- x+y
- x²+y²
- √(x²+y²)
- tan⁻¹(y/x)
Show answer and explanation
Answer: C. √(x²+y²)
r=|z|=√(x²+y²).
If z₁=r₁(cosθ₁+isinθ₁) and z₂=r₂(cosθ₂+isinθ₂), then z₁z₂ equals:
- r₁r₂e^(i(θ₁+θ₂))
- r₁r₂e^(i(θ₁−θ₂))
- r₁r₂/e^(i(θ₁+θ₂))
- r₁r₂/e^(i(θ₁−θ₂))
Show answer and explanation
Answer: A. r₁r₂e^(i(θ₁+θ₂))
Multiplying complex numbers multiplies magnitudes and adds arguments.
The real part of (1+7i)/(3−4i) is:
- 1/2
- 1
- −1/2
- −1
Show answer and explanation
Answer: D. −1
(1+7i)/(3−4i) × (3+4i)/(3+4i) = (3+4i+21i+28i²)/25 = (−25+25i)/25 = −1+i, so the real part is −1.
Given z₁=2(cos30°+isin30°) and z₂=3(cos60°+isin60°), find z₁z₂ in polar form.
Show model answer
z₁z₂ = (2×3)[cos(30°+60°)+isin(30°+60°)]
= 6(cos90°+isin90°)
Find modulus and argument of complex number 3+4i
Show model answer
Modulus = √(9+16) = 5
Argument = tan⁻¹(4/3) ≈ 53.13°
Sessions with Number Systems questions
| Session | Questions |
|---|---|
| 2026 Annual | 4 |
| 2025 1st Annual | 3 |
| 2025 2nd Annual | 5 |
| 2024 Annual | 3 |
| 2023 Annual | 2 |
Common questions
What does the Number Systems chapter cover on this page?
17 real Federal Board (FBISE) Mathematics questions on Number Systems from 2023 to 2026, for 11th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.
Other Mathematics chapters
- Differentiation 61
- Conic Sections 46
- Vectors 46
- Integration 39
- Functions and Limits 31
- Trigonometric Identities 30
- Matrices and Determinants 29
- Sequences and Series 28
- Introduction to Analytic Geometry 28
- Fundamentals of Trigonometry 26
- Quadratic Equations 21
- Binomial Theorem 20
- Permutation/Combination/Probability 19