B.Sc Method Chapter 1 (Complex Numbers) Notes

Sami Aslam

Mathematical Methods (B.Sc.)

Chapter:01 (Complex Numbers)

In this chapter, we will study the following topics:

equality of complex numbers
properties of complex numbers
associative law of addition
properties of multiplications
multiplicative identity
distributive law
left and right distributive laws
representationa of complex number
argand’s diagram
modulus of z
represtation of argand’s diagram
imaginary axis
trigonometric or polar form of a complex number
principal argument
product and quotient of a complex number in polar form
modulus and argument of given number
locus of a complex number
de moivre’s theorem
applications of de moivre’s theorem
roots of a complex number
the principal nth root
basic elementary functions
euler’s identity
euler’s formula
trigonometric functions
hyperbolic functions
relationships between trigonometric and hyperbolic functions
branch of logarithm
principal algorithm
inverse hyperbolic functions
inverse trigonometric functions
complex power
the principal value of a complex power
summation of series
sum of infinite series

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