Complex Numbers

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