Maths · Class 11 · Chapter 4
Complex Numbers and Quadratic Equations
12 lessons113 min5 simulations
This chapter builds the complex numbers a + ib, with i² = −1, so that equations such as x² + 1 = 0 and every quadratic with a negative discriminant have solutions. It sets up their arithmetic (sum, product, inverse, quotient and powers of i), square roots of negative numbers, the modulus and the conjugate, and the picture of each complex number as a point of the Argand plane.
Also called: complex numbers · quadratic equations · Argand plane
Lessons
12 lessons · 113 min
01Why new numbers are neededNCERT §4.18 min02The imaginary unit i and complex numbersNCERT §4.27 min03Adding and subtracting complex numbersNCERT §4.3.18 min04Multiplying complex numbersNCERT §4.3.37 min05Dividing and the multiplicative inverseNCERT §4.3.47 min06Powers of iNCERT §4.3.510 min1 sim07Square roots of negative numbersNCERT §4.3.610 min1 sim08Algebraic identities for complex numbersNCERT §4.3.77 min09Modulus and conjugateNCERT §4.410 min1 sim10The Argand planeNCERT §4.511 min1 sim11Quadratics with a negative discriminantNCERT §4.112 min1 sim12Chapter reviewMust-know facts, traps and formulas16 min
Simulations
5 in this chapter
Powers of i go round in foursIn: Powers of iWhen √a × √b is not √(ab)In: Square roots of negative numbersMultiplying by the conjugate makes a real numberIn: Modulus and conjugatePoints of the Argand planeIn: The Argand planeWhere the roots go when D turns negativeIn: Quadratics with a negative discriminant