definition , euler formula and application of complex number

1. SARASWATHY S

2.  INTRODUCTION
 COMPLEX NUMBER
 ROTATIONS OF i
 COMPLEX NUMBER IN POLAR FORM
 EULER FORMULA
 DE MOVIRE’S THEOREM
 COMPLEX FUNCTIONS
 APPLICATIONS

3. INTRODUCTION
 COMPLEX NUMBERS were first introduced by an
Italian mathematician GEROLAMO CARDANO,
during his attempt to solve cubic equations in the
16th century.
 The rules of addition,
subtraction,multiplication,division of complex
number were developed by Italian mathematician
RAFAEL BOMBELI .

4. DEFINITION OF COMPLEX
NUMBER

5. Real numbers and imaginary numbers are
subsets of the set of complex numbers.
Numbers

6. THE ROTATIONS OF i

7. Expressing Complex Numbers
in Polar Form
 THE POLAR FORM OF COMPLEX NUMBER
)

8. EULER FORMULA
 The polar form of a
complex number can be
written as
z=r
=r

9. De Moivre’s Theorem
De Moivre's Theorem shows us how to take complex
numbers to any power easily.
De Moivre's Theorem – Let r(cos F+isin F) be a complex
number and n be any real number. Then
[r(cos F+isin F]n = rn(cos nF+isin nF)
What is this saying?
The resulting r value will be r to the nth power and
the resulting angle will be n times the original angle.

10. Complex Functions
 A complex function is a function whose domain and
range subsets of the complex plane.
and

11. APPLICATIONS
 Complex numbers are
mainly used in Electrical
Engineering
techniques,because
FOURIER
TRANSFORMS are used
in understanding
oscillations and wave
behaviour that occur
both in AC current and
in modulated signals.
 Complex Analysis is used
when we launch a
satellite by
transformation or
mapping