Master Unit 1 Complex Numbers (NBF/FBISE new book 2025-2026) with concise solutions. Aim 90+ marks.
hsanotes.com Features:
- Updated for new book session 2025-2026
- Solved Ex 1.1–1.3 + Miscellaneous
- Quick powers of i, conjugates, inverses
- Additive & multiplicative inverse proofs
- Complex plane plotting points
- Factorization a² + b²
- Systems of complex equations
- Electrical circuit examples
Target: FBISE students & affiliated schools – Army Public School, Fazaia Inter College, Beaconhouse, Roots Millennium, The City School, Lahore Grammar School, Karachi Grammar School, OPF Boys/Girls College, Bahria College, PAF College.
Key Solved Examples (short form):
- Ex 1.1 Q1(i) √−3 = i√3 → y = √3
- Q1(ii) 6√−4 = 12i → y = 12
- Q1(iii) √−4/9 = (2/3)i → y = 2/3
- Q1(iv) −√−20 = −2i√5 → y = −2√5
- Q1(v) 4 − √−60 = 4 − 2i√15 → y = −2√15
- Q1(vi) √−8 · √−2 = −4 → y = 0
- Q2(i) (4−i)+(5+5i) = 9+4i
- Q2(v) (2+4i)(1+2i) = −6+8i
- Q3(i) i⁹ = i
- Q3(iii) i²⁸ = 1
- Q4(i) 9 + i⁶ = 8
- Q5(i) 3/(4−i) = (12/17) + (3/17)i
Useful Links:
- FBISE official: https://www.fbise.edu.pk
- National Book Foundation (NBF): https://www.nbf.org.pk
- Army Public Schools: https://apsacssectt.edu.pk
- Beaconhouse: https://www.beaconhouse.net
View PDF for full solutions, graphs & tables.
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