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Complex Number

Name ID No.Md Rasadul Islam 10116034Mahay Alam Noyon 10116024Ahasanul Mahbub

Jubayer10116011

Md Rahat Hossain 10116006Ashraful Alim 10116029

Group Members

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Complex Number

Presented By

Md Rasadul Islam

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• An ordered pair of real number generally written in the form “a+ib”

• Where a and b are real number and is an imaginary.

• In this expression, a is the real part and b is the imaginary part of complex number.

Complex Numbers

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When we combine the real and imaginary number then complex number is form.

Complex Number

Real Numb

er

Imaginary

Number

Complex

Number

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Complex Number• A complex number has a real part and an

imaginary part, But either part can be 0 .• So, all real number and Imaginary number are

also complex number.

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Complex Number

Complex number extend the concept of one-dimensional number line to the two-dimensional complex plan.

• Horizontal axis use for real part. • Vertical axis for the imaginary part.

7(Complex Number) 7

Equations like x2=-1 do not have a solution within the real numbers

12 x

1x

1i

12 i Real no:

Imaginary no:

Why complex numbers are introduced???

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THE POWERS OF i: then,1- If i

12 i ii 3 14 i ii 5

16 i ii 7 18 i .etc

9(Complex Number)

iii

)53()12()51()32(

i83

Example

Real Axis

Imaginary Axis

1z

2z

2zsumz

Addition : Complex number added by adding real part in real and imaginary part in imaginary.

(a + b) + (c + d ) = (a + c) + (b + d)

Fundamental Operations with complex number

(Complex Number) 10

Subtraction: Similarly, subtraction is defined (a + b) - (c + d ) = (a - c) + (b - d) .

ii

ii

21)53()12()51()32(

Real Axis

Imaginary Axis

1z

2z

2z

diffz

2z

Example

11(Complex Number)

Multiplication:

The multiplication of two complex number is define by the following formula:

(a + b).(c + d ) =(ac - bd) + (b c + ad) Square of the imaginary unit is -1.

²== -1

ii

ii

1313)310()152(

)51)(32(

Example

(Complex Number) 12

Division:Division can be defined as:

𝑎+𝑏𝑖  𝑐+𝑑𝑖  =¿ () + (

EXAMPLE i

i2176

i

iii

2121

2176

22

2

21147126

iii

415146

i

5520 i

55

520 i

i4

(Complex Number) 13

Examples of the application of complex numbers: 1) Electric field and magnetic field.2) Application in ohms law.

3) In the root locus method, it is especially important whether the poles and zeros are in the left or right half planes

4) A complex number could be used to represent the position of an object in a two dimensional plane,

How complex numbers can be applied to “The Real World”???

(Complex Number) 14

15(Complex Number)

Thank YouFOR YOUR ATTENTION..!