CBSE · Class 6-12

Class 11 · Mathematics (041)

Unit 4 · Class 11Mathematics (041)

Algebra

Complex Numbers and Quadratic Equations

Complex numbers, Argand plane, modulus, conjugate, and complex roots of quadratics.

Formative-only for boards

Polar representation of complex numbers
Fundamental Theorem of Algebra

Learn these concepts — they won't appear in the CBSE 2026-27 board paper.

Lessons

4 concepts

1
Complex Numbers
$z = a + ib$ where $i^2 = -1$ . Addition and multiplication distribute normally.
2
Modulus & Conjugate
$|z| = \sqrt{a^2 + b^2}$ ; $\bar z = a - ib$ ; $z \bar z = |z|^2$ .
3
Argand Plane
Plot $z = a + ib$ as $(a, b)$ . Geometric meaning of addition (parallelogram) and multiplication (rotation + scaling).
4
Quadratic Equations with Complex Roots
$ax^2 + bx + c = 0$ has roots $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . When discriminant $< 0$ , roots are complex conjugates.

Skills to practise

Skill · medium

Complex Numbers and Quadratic Equations — Practice (coming soon)

Practice bank for this unit is in progress. You can still read the lessons above.