Complex Numbers

Formulas are organized based on their importance in the CAT exam.
1 Locus in the Complex Plane
2 Reverse Triangle Inequality Applications
3 Triangle Inequality Applications
4 Cube Roots of Unity
5 Roots of a Complex Number
6 Euler's Formula
7 Properties of Modulus
8 Multiplication of Complex Numbers
9 Real and Imaginary Parts Using Conjugate
10 De Moivre's Theorem
11 Argument of a Complex Number
12 Algebraic Form of a Complex Locus
13 Division of Complex Numbers
14 Geometrical Interpretation of Multiplication
15 Locus Involving Argument
16 Circle in Complex Form
17 Powers of i
18 Quadratic Equation and Complex Roots
19 Multiplication in Polar Form
20 Complex Number in Cartesian Form
21 Modulus of Sum and Difference
22 Sum and Product of Conjugate Roots
23 Unit Complex Number
24 Distance Between Two Complex Numbers
25 Properties of Conjugate
26 Rotation in Complex Plane
27 Complex Number as a Vector
28 Equation of Circle
29 Distance-Based Loci
30 General Roots of Unity
31 Modulus of a Complex Number
32 Argument Properties
33 General Quadratic Root Relations
34 Distance Between Complex Numbers
35 Modulus Identities
36 Properties of Cube Roots of Unity
37 Euler's Formula
38 Modulus of Complex Number
39 Complex Conjugate
40 Important Conjugate Identities
41 Reciprocal of a Complex Number
42 Addition and Subtraction
43 Product and Quotient of Modulus
44 Equality of Complex Numbers
45 Properties of Modulus
46 Complex Inequalities
47 Important Modulus Identity
48 Complex Number
49 Division in Polar Form
50 Polynomial Factor from Conjugate Roots
51 Argand Plane
52 Cube Roots of Unity
53 Geometrical Interpretation of Division
54 Exponential Form
55 Polar Form
56 Definition of Complex Number
57 Polar Form of a Complex Number
58 Argument of Complex Number
59 De Moivre's Theorem
60 Conjugate of a Complex Number
61 Square of a Complex Number
62 Polynomial Equation with Real Coefficients