Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations – Revision Notes

Quick revision notes for Class 11 Maths Chapter 4 (Complex Numbers and Quadratic Equations). These Class 11 Maths Chapter 4 notes are ideal for quick revision just before exams.

Imaginary Unit

• i = √(−1); i²=−1; powers cycle every 4 (i,−1,−i,1).

Complex Numbers

• z = a+bi; conjugate z̄=a−bi; modulus |z|=√(a²+b²).
• z×z̄ = |z|².

Operations

• Add/subtract: combine real & imaginary parts separately.
• Multiply: use i²=−1 to simplify.

Quadratic Equations

• D=b²−4ac < 0 → complex conjugate roots.
• x = [−b ± √D]/2a.

One-Line Summary

Complex numbers (a+bi, with i²=−1) extend the real number system so every quadratic equation has solutions, with negative-discriminant quadratics always yielding conjugate pairs of complex roots.

Written by Satish

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