﻿ Page 1 - Chapter 2. Complex Numbers and Quadratic Equations
Basic HTML Version View Full Version
Page 1 - Chapter 2. Complex Numbers and Quadratic Equations
P. 1

``````CHAPTER 2

Complex Numbers and Quadratic Equations

Topics

•   Complex numbers as ordered pairs of reals
•   Representation of complex numbers in the form	   +      and their representation in a plane
•   Argand diagram
•   Algebra of complex numbers
•   Modulus and argument (or amplitude) of a complex number
•   Square root of a complex number
•   Triangle inequality
•   Quadratic equations in real and complex number system and their solutions
•   Relation between roots and co-efficient, nature of roots
•   Formation of quadratic equations with given roots
Key Notes

Complex  Numbers  as  Ordered  Pairs  of              The complex number is represented by the real numbers (x,
Reals                                                 y) in a x-y plane and it is referred to as the complex plane or
-plane.
A  complex  number  z  is  defined  as  an  ordered  pair.  It  is
given by,                                             |z| is modulus of the complex number that gives the vector
representation.
= (  ,   )
arg z is the angle made by the complex number along the
where    and    are a pair of real numbers.           plane.
Sometimes  the  order  pairs  of  real  numbers  are  given  by   Argand Diagram
(  ,   ) which are called the polar coordinates of the point.
The plane having a complex number assigned to each of its
The polar form is represented by,                     point is called the complex plane or the Argand plane.

=   (cos    +    sin   )             The representation of a complex number z = x + iy and its
Representation  of  Complex  Numbers  in              conjugate z = x – iy in the Argand plane is,
the form a+ib and their Representation in
a Plane

Complex number is represented in the form of	   +     ,    is
the  real  part  and      is  the  imaginary  part  of  the  complex
numbers. They are denoted by Re    and Im    respectively.

Geometrically, the point (x, – y) is the mirror image of the
point (x, y) on the real axis.
P (x, y) is the real axis and Q (x, -y) is the imaginary axis.

Algebra of Complex Numbers

Year Book Maths 2021`````` 1   2   3   4   5   6 