Complex Numbers and Quadratic Equations

Since $x^2 + 1 = 0$ has no real solution, mathematics builds a bigger system where it does: complex numbers $a + ib$ with $i^2 = -1$. Covers their arithmetic, powers of $i$, modulus and conjugate, the Argand plane, and quadratic equations with negative discriminant — a JEE Main fixture from modulus computations to cube roots of unity.