NDA Maths · Teaching notes
Complex Numbers — NDA Mathematics
Complex Numbers is around 72 past-year NDA questions built on one idea: i² = −1 turns every quadratic into something solvable and puts numbers on a plane. Work the three notes in order — first the fundamentals, conjugate, modulus and argument (the Argand-plane geometry); then powers of i and De Moivre's theorem for roots; and finally the cube roots of unity, whose identities (ω³ = 1 and 1 + ω + ω² = 0) answer a large, predictable family of questions. The recurring trap is the principal argument's quadrant — always place the number on the plane before reading off its angle.
Subtopic notes
Modulus, Argument & Conjugate
39 PYQsThe core toolkit of a complex number: its conjugate, its modulus (distance from the origin), and its argument (angle on the Argand plane) — plus the conditions that make it purely real or purely imaginary.
Open note
Powers of i, De Moivre & Roots
15 PYQsThe four-step cycle of powers of i, De Moivre's theorem for raising complex numbers to powers, and finding square/nth roots of a complex number.
Open note
Cube Roots of Unity
18 PYQsThe three cube roots of 1 — namely 1, ω, ω² — and the two identities (ω³ = 1 and 1 + ω + ω² = 0) that answer a large, predictable family of NDA questions.
Open note
PYQ weightage by concept
8 concepts · 72 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
8 concepts · 72 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| Modulus and the triangle inequality | 18 | 25% |
| Conjugate; purely real / purely imaginary | 10 | 14% |
| Argument and polar form | 9 | 13% |
| What a complex number is | 2 | 3% |
| Concept | PYQs | Share |
|---|---|---|
| Powers of i (the period-4 cycle) | 10 | 14% |
| De Moivre's theorem and roots | 5 | 7% |
| Concept | PYQs | Share |
|---|---|---|
| Applying ω: powers, expressions, related roots | 15 | 21% |
| 1, ω, ω² and their identities | 3 | 4% |