This page will teach you how to master JEE Complex Numbers up to JEE Advanced level. We highlight the main concepts, provide a list of examples with solutions, and include problems for you to try. Once you are confident, you can take the quiz to establish your mastery.
To have mastery over Complex Numbers for JEE Advanced, the main concepts you should be confident of are square root of a complex number, logarithm of a complex number, modular inequalities, De Moivre's theorem and rotation of a complex number.
∣z1+z2∣2=∣z1∣2+∣z2∣2⇔z2z1 is purely imaginary number
De Moivre's theorem
(cosθ+isinθ)n=cosnθ+isinnθ, when n is an integer
cosnθ+isinnθ is one of the values of (cosθ+isinθ)n, when n is a fraction
Rotation of a complex number
When we rotate z1 through an angle θ in anticlockwise direction about origin (0,0), say we get z2, then z1−0z2−0=∣z1−0∣∣z2−0∣eiθ
When we rotate z1 through an angle θ in anticlockwise direction about another complex number z0, say we get z2, then z1−z0z2−z0=∣z1−z0∣∣z2−z0∣eiθ