Complex Numbers

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