Attend Live Classes using Any Device be it Phone, Tablet or Computer

Get Started Today

2.1 - Algebra of Complex Numbers.pdf

Complex numbers

Report

Add to classroom

Arumugam R

Mathematics Intrested

Study Material

3.1.3 multiple and submultiple angles 3A.pdf

af

Mathematics

0 Likes

14 Views

Copied to clipboard

Arumugam R

Nov 19, 2021

Study Material

3.1.3 multiple and submultiple angles 3A.pdf

af

Mathematics

0 Likes

46 Views

Copied to clipboard

Arumugam R

Nov 19, 2021

Study Material

3.1.2 multiple and submultiple angles 2A.pdf

af

Mathematics

0 Likes

15 Views

Copied to clipboard

Arumugam R

Nov 19, 2021

Study Material

3.1.2 multiple and submultiple angles 2A.pdf

af

Mathematics

0 Likes

49 Views

Copied to clipboard

Arumugam R

Nov 19, 2021

Study Material

3.1.1 sum difference angles formulae and problems.pdf

af

Mathematics

0 Likes

35 Views

Copied to clipboard

Arumugam R

Nov 15, 2021

Study Material

3.1 formulae.pdf

af

Mathematics

0 Likes

40 Views

Copied to clipboard

Arumugam R

Nov 15, 2021

Study Material

3.1 - Compound Angles.pdf

class-2nd

Mathematics

1 Likes

106 Views

Copied to clipboard

Arumugam R

Nov 10, 2021

Study Material

Model Questn..pdf

af

Mathematics

0 Likes

23 Views

Copied to clipboard

Arumugam R

Oct 29, 2021

Study Material

Model Questn..pdf

af

Mathematics

0 Likes

59 Views

Copied to clipboard

Arumugam R

Oct 29, 2021

Study Material

2.2 - De-Moivre's Theorem.pdf

af

Mathematics

0 Likes

20 Views

Copied to clipboard

Arumugam R

Oct 26, 2021

Study Material

2.2 - De-Moivre's Theorem.pdf

af

Mathematics

0 Likes

154 Views

Copied to clipboard

Arumugam R

Oct 26, 2021

Homework

Mathematics-1

class-2nd

Mathematics

0 Likes

21 Views

Copied to clipboard

Arumugam R

Oct 25, 2021

Homework

Mathematics -1

af

Mathematics

0 Likes

23 Views

Copied to clipboard

Arumugam R

Oct 25, 2021

Study Material

2.1 - Algebra of Complex Numbers.pdf

af

Mathematics

0 Likes

26 Views

Copied to clipboard

Arumugam R

Oct 21, 2021

Study Material

Argand diagram problems-compressed.pdf

class-2nd

Mathematics

0 Likes

56 Views

Copied to clipboard

Arumugam R

Oct 15, 2021

Study Material

Argand diagram problems-compressed.pdf

af

Mathematics

0 Likes

116 Views

Copied to clipboard

Arumugam R

Oct 15, 2021

Study Material

Complex numbers -Argand diagram-compressed.pdf

class-2nd

Mathematics

0 Likes

39 Views

Copied to clipboard

Arumugam R

Oct 15, 2021

Study Material

Complex numbers -Argand diagram-compressed.pdf

af

Mathematics

0 Likes

133 Views

Copied to clipboard

Arumugam R

Oct 15, 2021

Study Material

1.3 Binomial Theorem-compressed.pdf

class-2nd

Mathematics

0 Likes

52 Views

Copied to clipboard

Arumugam R

Oct 15, 2021

Study Material

1.3 Binomial Theorem-compressed.pdf

af

Mathematics

0 Likes

34 Views

Copied to clipboard

Arumugam R

Oct 15, 2021

Study Material

Complex analysis ponnusammy

class-2nd

Mathematics

7 Likes

1453 Views

Copied to clipboard

Sarthak Tiwari

Nov 23, 2021

Study Material

2.1 - Algebra of Complex Numbers

af

Mathematics

0 Likes

26 Views

Copied to clipboard

Arumugam R

Oct 21, 2021

Study Material

2.1 - Algebra of Complex Numbers

automationstudents

Maths

0 Likes

12 Views

Copied to clipboard

random

Feb 24, 2022

Study Material

5-COMPLEX NUMBERS AND QUADRATIC EQUATIONS

jee

Mathematics

0 Likes

0 Views

Copied to clipboard

PARVATHY ARUN

May 18, 2022

Study Material

5-COMPLEX NUMBERS AND QUADRATIC EQUATIONS

class-11th

Mathematics

0 Likes

0 Views

Copied to clipboard

PARVATHY ARUN

Oct 26, 2021

Study Material

Complex analysis

class-2nd

Mathematics

0 Likes

396 Views

Copied to clipboard

Sarthak Tiwari

Nov 23, 2021

Study Material

5-COMPLEX NUMBERS AND QUADRATIC EQUATIONS

keamcrash

Physics

0 Likes

1 Views

Copied to clipboard

PARVATHY ARUN

May 18, 2022

Study Material

COMPLEX NO.2

b-com

Mathematics

1 Likes

232 Views

Copied to clipboard

S

SREEJESH

Oct 16, 2021

Study Material

(complex number)

b-com

Maths

1 Likes

7 Views

Copied to clipboard

Score High Institute

Feb 03, 2022

Study Material

Maths Revision.in

class-12th

Maths

0 Likes

48 Views

Copied to clipboard

H

H.S.S Tuition Centre

Jan 11, 2022

Study Material

complex number-study pira

jee

Mathematics

0 Likes

7 Views

Copied to clipboard

IITian neeraj kumar

Mar 16, 2022

Study Material

James And Churchill complex analysis

class-2nd

Mathematics

0 Likes

197 Views

Copied to clipboard

Sarthak Tiwari

Nov 23, 2021

Study Material

Comples numbers 1

class-2nd

Mathematics

0 Likes

15 Views

Copied to clipboard

N

Neeha Sherin

Dec 19, 2021

Study Material

class2

class-11th

Mathematics

0 Likes

6 Views

Copied to clipboard

M

Minu Thambi V

Jan 24, 2022

Study Material

Engineering-Mathematics-I

b-tech

English

1 Likes

122 Views

Copied to clipboard

N

Nivedha Murukesan

Oct 18, 2021

Homework

Mathematics -1

af

Mathematics

0 Likes

23 Views

Copied to clipboard

Arumugam R

Oct 25, 2021

Homework

Complex Number

class-11th

Mathematics

0 Likes

2 Views

Copied to clipboard

Ravi

Jan 12, 2022

Test

Weekly Test -6

b-com

Pcm

0 Likes

15 Views

Copied to clipboard

Shiv Narayan Kumar

Oct 15, 2021

Study Material

Complex Variables

b-sc

Complexanalysis

0 Likes

64 Views

Copied to clipboard

Ashok Kumar

Feb 09, 2022

Test

Complex Numbers

class-11th

Maths

0 Likes

16 Views

Copied to clipboard

R

Rukhsar

Oct 21, 2021

Pdf Description

Page 1 :

DEFINITION : COMPLEX NUMBER, A number which is of the form a + ib, where a and b are real numbers is called a, , complex number. It is denoted by z and i = v-1 is called as Imaginary unit., , consider the complex number z=a+, , ib, , Real part ofz =a + ib is 'a' and it is denoted by Re(), Imaginary part ofz = a+ib is 'b' and it is denoted by Im(z), , For example:, , z= 2+3i, then Re(z) =2, Im (2) = 3, , NOTE, 1. A complex number z is said to be real if Im(2) = 0, 2. A complex number z is said to be purely imaginary if Re(z) = 0, , MATH FACT, Zero is the only number which is at once real and purely imaginary, , im, , a + ib, , DEFINITION: CONJUGATE, The Conjugate of the complex number, , z=a + ib is defined as the complex number, a-ib and it is denoted by, Z=a-ib., i.e., conjugate of a complex number is obtained by, , changing the sign of imaginary part of z., , e, , a- ib

DEFINITION : COMPLEX NUMBER, A number which is of the form a + ib, where a and b are real numbers is called a, , complex number. It is denoted by z and i = v-1 is called as Imaginary unit., , consider the complex number z=a+, , ib, , Real part ofz =a + ib is 'a' and it is denoted by Re(), Imaginary part ofz = a+ib is 'b' and it is denoted by Im(z), , For example:, , z= 2+3i, then Re(z) =2, Im (2) = 3, , NOTE, 1. A complex number z is said to be real if Im(2) = 0, 2. A complex number z is said to be purely imaginary if Re(z) = 0, , MATH FACT, Zero is the only number which is at once real and purely imaginary, , im, , a + ib, , DEFINITION: CONJUGATE, The Conjugate of the complex number, , z=a + ib is defined as the complex number, a-ib and it is denoted by, Z=a-ib., i.e., conjugate of a complex number is obtained by, , changing the sign of imaginary part of z., , e, , a- ib

Page 2 :

Basic Algebraic operations of complex numbers:, Addition oftwo complex numbers, If, z = a + ib and z2 =c+ id, then, Z1t Z2 = (a + ib) + (c + id), Z1t Z2 = (a + c) + i(b+d), , MATH FACT, 0=0+0i is known as additive identity and, , -Zis called as the additive inverse of Z., Subtraction of two complex numbers, , Ifz, , =, , a+iband z2, , =, , c +, , id, then, , Z1 2 2 ( a + ib) - (¢ + id), , Z1-2 (a-c)+ i(b -d)|, , <86, , Multiplication of complex number z by, Multiplication of a complex number z by i' is, , a rotation of z by 90° or, , radians in the counter, , clockwise direction about the origin., , Multiplication of two complex numbers, , Ifz =a+ib and z2 =c+ id, then, Z1Z2, , (a + ib) (c +id), ac, , iad + ibc + itbd, , ac +i(ad + bc) - bd, , Z122, , (ac - bd) + i(ad + be)|, , ii= -1)

Basic Algebraic operations of complex numbers:, Addition oftwo complex numbers, If, z = a + ib and z2 =c+ id, then, Z1t Z2 = (a + ib) + (c + id), Z1t Z2 = (a + c) + i(b+d), , MATH FACT, 0=0+0i is known as additive identity and, , -Zis called as the additive inverse of Z., Subtraction of two complex numbers, , Ifz, , =, , a+iband z2, , =, , c +, , id, then, , Z1 2 2 ( a + ib) - (¢ + id), , Z1-2 (a-c)+ i(b -d)|, , <86, , Multiplication of complex number z by, Multiplication of a complex number z by i' is, , a rotation of z by 90° or, , radians in the counter, , clockwise direction about the origin., , Multiplication of two complex numbers, , Ifz =a+ib and z2 =c+ id, then, Z1Z2, , (a + ib) (c +id), ac, , iad + ibc + itbd, , ac +i(ad + bc) - bd, , Z122, , (ac - bd) + i(ad + be)|, , ii= -1)

Page 4 :

4) If z = (3,-1) and z2 = (4,2) find 4z1 Z2, , Solution:, Given z, , =, , 3-i, , Z24+ 2i, 4z1 Z 2 = 4(3-i)-(4 + 2i), =, , 12-4i-4-2i, , 4z1-22= 8-6i, 5) Find the value of z1z, , if zj = 4 +i and z2 = 1 -i, , Solution:, Given z, , = 4+i and z2 = 1 -i, , Z172, , 4 +i) (1-i), , = 4-4i+i-?, , i=-1], , = 4-3i-(-1), , =4, , 3i +1, , Z1Z2=5-3i, 6) Find the real and imaginary parts o f, , Solution, Let z, , 5-2, 2x2, , 5-2, , +2, , (5+ 21), , I(a +ib) (a - ib) = (a)*+(61, , (S)2+ (2, 5+21, , 25+4, z 2, , Re(z) =, , 29, , Im(z) =, 7) Find the conjugate of, Solution:, , Let z, -21), = 15-101), , I:a+ ib) (a - ib) = (a)* +(6)], , (3)2+(2)2, , 15-10, 9+4, , 15-10i, 13, , Conjugateofz (7) =, , 8) Find the values of i + i^ + it, Solution:, = -1 +-1)G)+(1*, = -1-i+l, -1, , [i=-1]

4) If z = (3,-1) and z2 = (4,2) find 4z1 Z2, , Solution:, Given z, , =, , 3-i, , Z24+ 2i, 4z1 Z 2 = 4(3-i)-(4 + 2i), =, , 12-4i-4-2i, , 4z1-22= 8-6i, 5) Find the value of z1z, , if zj = 4 +i and z2 = 1 -i, , Solution:, Given z, , = 4+i and z2 = 1 -i, , Z172, , 4 +i) (1-i), , = 4-4i+i-?, , i=-1], , = 4-3i-(-1), , =4, , 3i +1, , Z1Z2=5-3i, 6) Find the real and imaginary parts o f, , Solution, Let z, , 5-2, 2x2, , 5-2, , +2, , (5+ 21), , I(a +ib) (a - ib) = (a)*+(61, , (S)2+ (2, 5+21, , 25+4, z 2, , Re(z) =, , 29, , Im(z) =, 7) Find the conjugate of, Solution:, , Let z, -21), = 15-101), , I:a+ ib) (a - ib) = (a)* +(6)], , (3)2+(2)2, , 15-10, 9+4, , 15-10i, 13, , Conjugateofz (7) =, , 8) Find the values of i + i^ + it, Solution:, = -1 +-1)G)+(1*, = -1-i+l, -1, , [i=-1]

Page 5 :

9) Find the real and, , 7+21, , imaginary parts, , of-3, -3, , Solution:, Let, , z, , 2, , =, , 2-31, , 7+22t+3/), 2-3 (2+ 3i), 14+21+4i+612, , (2)2+(3), , I(a +ib) (a - ib) = (a) +(b}], , 14+251+6() j2 1, 14+25i-6, 8+25i, 13, , Re(z)=, , Im(2) =, , 10/75, , 13, , 10) Express 4 t i n a + i b form, 3-4, , Solution:, Let, , z, , =2x4-3)4L,, G+4), 4+31 (4- 31) 3 - 4 " (3+41), +3i+, , 4j2, , (a +ib) (a-ib) = (a)*+ (b)°1, , (4)+(32 3+(4, 8-6 3i+4(-1), , 16+9, , :f-1, , 9+16, , = 861+ 31-4, 25, , 4-3, 25, , 25, , 25, , a+ibform, , I1) Find the real and imaginary parts of, , 2+9, (1+41), , Solution:, Let z = *D2+1D, (1+41), , - 2+i+2i+12, (1+4i), , 3i-1, , (1+41), 1+3i, 1+41, E, , 1+3(1-41), 1+4i (1- 4i), 4i+3i-12i2, (1)2 +(4)2, , = +12, 16, Z, , 13 -i, 17, , . Re(z) =, Im (z) =, 17, , (a+ib) (a - ib) = (a)+ (b)1, , [i-1]

9) Find the real and, , 7+21, , imaginary parts, , of-3, -3, , Solution:, Let, , z, , 2, , =, , 2-31, , 7+22t+3/), 2-3 (2+ 3i), 14+21+4i+612, , (2)2+(3), , I(a +ib) (a - ib) = (a) +(b}], , 14+251+6() j2 1, 14+25i-6, 8+25i, 13, , Re(z)=, , Im(2) =, , 10/75, , 13, , 10) Express 4 t i n a + i b form, 3-4, , Solution:, Let, , z, , =2x4-3)4L,, G+4), 4+31 (4- 31) 3 - 4 " (3+41), +3i+, , 4j2, , (a +ib) (a-ib) = (a)*+ (b)°1, , (4)+(32 3+(4, 8-6 3i+4(-1), , 16+9, , :f-1, , 9+16, , = 861+ 31-4, 25, , 4-3, 25, , 25, , 25, , a+ibform, , I1) Find the real and imaginary parts of, , 2+9, (1+41), , Solution:, Let z = *D2+1D, (1+41), , - 2+i+2i+12, (1+4i), , 3i-1, , (1+41), 1+3i, 1+41, E, , 1+3(1-41), 1+4i (1- 4i), 4i+3i-12i2, (1)2 +(4)2, , = +12, 16, Z, , 13 -i, 17, , . Re(z) =, Im (z) =, 17, , (a+ib) (a - ib) = (a)+ (b)1, , [i-1]

Attend Live Classes using Any Device be it Phone, Tablet or Computer

Get Started Today

Get Started Today

https://teachmint.storage.googleapis.com/public/119790726/StudyMaterial/644bc5d0-6db6-4687-bb02-2e8319d6ddb5.pdf

61712f0985e1dbdc5db3c21e

4de3bf1a-fb10-4276-9e7e-1a4c07220c51

Teachmint is an education infrastructure provider and the creator of
one of the largest teaching platforms in the world.

Contact Us

Enzyme Park View #1604, 1st Floor 25th Main, 22nd Cross Rd,
Sector 2, HSR Layout, Bengaluru, Karnataka 560102

contact@teachmint.com

08035073710 (8 AM - 8 PM Everyday)

©Copyright
, Teachmint Technologies Pvt. Ltd.