ORDERED PAIR, CARTESIAN PRODUCT OF SETS ,DEFINITION OF RELATION
Relations and its types
DOMAIN , CO-DOMAIN AND RANGE OF RELATION
DEFINITION OF FUNCTION
DOMAIN , CO-DOMAIN AND RANGE OF FUNCTION
REAL VALUED FUNCTION
CONSTANT FUNCTION
ZERO FUNCTION
IDENTITY FUNCTION
SIGNUM FUNCTION
POLYNOMIAL FUNCTION
EXPONENTIAL FUNCTION
LOGARITHMIC FUNCTION
GREATEST INTEGER FUNCTION
MODULUS FUNCTION
SUM, DIFFERENCE, PRODUCT & QUOTIENTS OF FUNCTION
Introduction to the Complex number
Algebra of two complex numbers
The square root of a complex number
Argand plane and Polar representation
The modulus and argument of a complex number
Introduction to sequence
Introduction to series
Arithmetic progression and Arithmetic mean
Geometric progression and geometric mean
Relation between A.M and G.M
Sum to n terms of special cases
DETERMINANTS AND MATRICES
Determinant of a 3*3 matrix
Properties of determinants
Minors and co-factors
Notation and order of Matrices
Algebra of matrices
Adjoint of a Matrix
Solving system of equations
Limits
Algebra of limits
Limits of polynomial and rational function
Limits of trigonometric functions
Integration Basic Definition
Properties of definite integral
Integration By Substitution Method
Integration Using Trigonometric Identity
Integrals Of Some Particular Functions
Integration By Partial Fractions
Integration By Parts Rule
Integrals Of Some Type
Definite integrals definition
Evaluation Of Definite Integral By Substitution
Some Properties Of Definite Integrals
A complex number is defined as z=x+yi, where 
and 
are real values. The most important property of a complex number is 
We can also represent any complex number in an ordered pair of real numbers 
For example, 
is also written as 
.
The most important property of a complex number is to remember that,
Similar way, we can also use
,
,
, and so on.
Conjugate of a complex number is a number with the same imaginary number with opposite sign of a given complex number with the same real number and it’s sign. It is denoted as 
. It is also known as the multiplicative inverse of the complex number.
Let’s consider some examples:
1. Find the complex conjugate of 
.
A complex number may be a purely real number if its imaginary part is zero. The complex number is said purely imaginary number if its real part is zero.
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