NCERT Mathematics, Class 11, textbook pages 76–88

How to help your child with Class 11 Maths Chapter 4, Complex Numbers and Quadratic Equations, at home

i, complex numbers and roots of quadratics, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

3 + 4i|z| = 5ReIm

NCERT Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations: what it teaches

When a quadratic has a negative discriminant, its roots are complex. Your teen learns i = √−1, algebra of complex numbers, modulus and conjugate, the Argand plane, and solves quadratics with complex roots.

Why it matters later. Complex numbers are important in engineering, physics and higher mathematics.

See it: this chapter in pictures

i¹ = i, i² = −1i³ = −i, i⁴ = 1repeats every 4
The cycle of 4.
(3 + 2i)(1 − i)= 3 − 3i + 2i − 2i²= 5 − i
Use i² = −1.
x² + x + 1 = 0D = −3x = (−1 ± i√3)/2
Negative discriminant: complex roots.

You need

  • graph paper for the Argand plane
  • a calculator

Tonight’s 45 minutes

  1. Compute i², i³, i⁴ and find the pattern.
  2. Add, multiply and divide (3 + 2i) and (1 − i).
  3. Plot 3 + 4i on the Argand plane and find its modulus (5).
  4. Solve x² + x + 1 = 0.

Words to use

  • imaginary unit
  • complex number
  • real part
  • imaginary part
  • conjugate
  • modulus
  • Argand plane

Watch for

  • Writing √−4 × √−9 = √36 = 6. √−4 = 2i, √−9 = 3i, product = 6i² = −6.
  • Forgetting to multiply by the conjugate when dividing. Multiply top and bottom by the conjugate.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

Youi⁵⁷?

Your child57 = 4 × 14 + 1, so i.

A game for this week: Powers of i

  1. Call a large power like i⁵⁷.
  2. Players reduce the exponent mod 4.
  3. Give the value.
  4. Fastest correct wins.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Electrical engineering.
  • Signal processing.
  • Computer graphics.
  • Physics of waves.

Quick check

Ask these at the end of the week. Tap to see the answer.

i⁴?

1.

Modulus of 3 + 4i?

5.

Roots of x² + x + 1 = 0?

(−1 ± i√3)/2.

Ready for the next chapter when your child…

  • Computes with complex numbers.
  • Finds modulus and conjugate.
  • Solves quadratics with complex roots.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 11). See the full Class 11 parent guide for every chapter.

Questions parents ask

What is i?

A number with i² = −1.

What is the conjugate of a + bi?

a − bi.

Why are complex numbers useful?

They solve all quadratics and model waves and circuits.