Complex Numbers

Complex numbers explained with definitions, algebraic operations, polar form, and simple examples for clear conceptual understanding.

1.Introduction to Complex Numbers

Introduction to complex numbers for Class 11: need for complex numbers, imaginary unit i, a + ib form, and real & imaginary parts with simple examples.

2.Algebra of Complex Numbers

Learn the algebra of complex numbers: addition, subtraction, multiplication, division, conjugate, rationalisation, and powers of i with clear examples.

3.Modulus and Argument

Understand modulus and argument of complex numbers with Argand plane representation, quadrant-wise angles, principal argument, and clear step-by-step examples.

4.Polar Form of Complex Numbers

Learn how to express complex numbers in polar form r(cosθ + i sinθ), convert between Cartesian and polar forms, and use geometric understanding with examples.

5.De Moivre’s Theorem

Understand De Moivre’s Theorem with definition, geometric idea, applications to powers of complex numbers, and deriving useful trigonometric identities.

6.nth Roots of Unity

Learn the concept of nth roots of unity with their formula, geometric representation on the unit circle, cube roots of unity, and algebraic properties.