← CBSE Class 11
Complex Numbers and Quadratic Equations
Chapter Overview
A complex number is a + ib where i = √(-1). The chapter covers algebra of complex numbers, conjugate, modulus, and representation on the Argand plane. Polar form and De Moivres theorem for powers and roots are introduced. Quadratic equations with complex roots are solved using the quadratic formula.
Topics Covered
- Imaginary Numbers and i
- Standard Form a + ib
- Algebra of Complex Numbers
- Conjugate and Modulus
- Argand Plane
- Polar Form
- De Moivres Theorem
- Square Roots
- Quadratic Equations
Key Formulas
i2 = -1
|z| = √a2 + b2
z x conjugate(z) = |z|2
Polar: z = r(cos A + i sin A)
De Moivre: (cos A + i sin A)n = cos(nA) + i sin(nA)
x = (-b +/- √b2 - 4ac)/2a
Real-World Applications
Applications: Electrical engineering (AC circuits), quantum mechanics, signal processing, control theory.
Study Tips
Tip: Master basic algebra first
Tip: Polar form simplifies powers and roots
Tip: Visualize on the Argand plane