Cue Column:

• What are the three representations?
• When to use which form?
• What's the exam weightage?

Note Column: Complex numbers appear in 2-3 JEE Main questions yearly. The chapter has three representation modes: (1) Algebraic: z = a + ib for addition/subtraction and conjugate operations; (2) Polar/Euler: z = re^(i*theta) for multiplication, division, powers, and roots; (3) Geometric: Argand plane for locus, distance, and angle problems. The golden rule: choose the representation that makes the operation simplest. Multiplication/division -> polar. Locus -> geometric. Algebraic manipulation -> Cartesian. Most JEE questions combine two representations.

Summary: Three modes: algebraic, polar, geometric. Switch between them based on the operation required.