Maths · Class 11 · Chapter 4
Complex Numbers and Quadratic Equations
12 lessons 104 min 2 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.
What the exam asks
JEE Main asks you to reduce powers of i, to put products and quotients into the form a + ib using the conjugate, to equate real and imaginary parts to find unknowns, to use |z₁z₂| = |z₁||z₂| and zz̄ = |z|², to read numbers as points, distances and mirror images on the Argand plane, and to solve quadratics with D < 0. Marks are lost on applying √a √b = √(ab) with both numbers negative, on the sign of i³, on writing Im z as ib instead of b, and on forgetting that the roots of a real quadratic with D < 0 come as a conjugate pair.
Lessons
12 lessons · 104 min
1Why new numbers are neededNCERT §4.18 min2The imaginary unit i and complex numbersNCERT §4.27 min3Adding and subtracting complex numbersNCERT §4.3.18 min4Multiplying complex numbersNCERT §4.3.37 min5Dividing and the multiplicative inverseNCERT §4.3.47 min6Powers of iNCERT §4.3.57 min7Square roots of negative numbersNCERT §4.3.67 min8Algebraic identities for complex numbersNCERT §4.3.77 min9Modulus and conjugateNCERT §4.47 min10The Argand planeNCERT §4.511 min 1 sim11Quadratics with a negative discriminantNCERT §4.112 min 1 sim12Chapter reviewMust-know facts, traps and formulas16 min