JEE Study Guide 5. Complex Numbers

Contents of the Chapter

5.1 Introduction
5.2 Integral powers of IOTA(i)
5.3 Imaginary quantities
5.4 Complex numbers
5.5 Equality of complex numbers
5.6 Addition of complex numbers
5.7 Subtraction of complex numbers
5.8 Multiplication of complex numbers
5.9 Division of complex numbers
5.10 Conjugate of a complex number
5.11 Modulus of a complex number
5.12 reciprocal of a complex number
5.13 Square roots of a complex number
5.14 Representation of a complex number
5.15 Argument or amplitude of a complex number z = x+iy for different signs of x and 5.16 Eulerian form of a complex number
5.17 Geometrical representations of fundamental operations
5.17B Modulus and argument of multiplication of two complex numbers
5.18 Modulus and argument of division of two complex numbers
5.19 Geometrical representation of conjugate of a complex number
5.20 Some important results on modulus and argument
5.21 Geometry of complex numbers
5.22 Affix of a point dividing the line segment joining points having affixes z1 and z2
5.23 Equation of the perpendicular bisector
5.24 Equation of a circle
5.25 Complex number as a rotating arrow in the argand plane
5.25B Some important results
5.26 Some standard loci in the argand plane
5.27 Equation of a straight line
5.28 De-moivere’s theorem
5.29 Roots of a complex number
5.30 Roots of unity
5.31 Cube roots of unity
5.32 Logarithm of a complex number


Study Plan

Day 1

5.1 Introduction
5.2 Integral powers of IOTA(i)
Example 1,2
5.3 Imaginary quantities
Ex 1 to 4
5.4 Complex numbers
Ex 1,2
5.5 Equality of complex numbers
Ex 1,2
5.6 Addition of complex numbers
Ex 1
5.7 Subtraction of complex numbers
Ex 1


Day 2

5.8 Multiplication of complex numbers
Ex 1, 2
5.9 Division of complex numbers
ex 1
5.10 Conjugate of a complex number
5.11 Modulus of a complex number
ex 1

Day 3
5.12 reciprocal of a complex number

5.13 Square roots of a complex number
ex 1 to 5

Day 4

Exercises


Day 5
5.14 Representation of a complex number

5.15 Argument or amplitude of a complex number z = x+iy for different signs of x and y
ex 1, 1 to 5

Day 6

5.16 Eulerian form of a complex number
ex. 1
5.17 Geometrical representations of fundamental operations
5.17B Modulus and argument of multiplication of two complex numbers
5.18 Modulus and argument of division of two complex numbers

Day 7

5.19 Geometrical representation of conjugate of a complex number
5.20 Some important results on modulus and argument


Day 8

5.21 Geometry of complex numbers
5.22 Affix of a point dividing the line segment joining points having affixes z1 and z2
ex 1 to 5

Day 9

5.23 Equation of the perpendicular bisector
5.24 Equation of a circle
Ex 1 to 10.

Day 10

5.25 Complex number as a rotating arrow in the argand plane
ex 1 to 11
5.25B Some important results
ex 1 to 4

Day 11

5.26 Some standard loci in the argand plane
ex 1,2
5.27 Equation of a straight line
ex 1,1

Day 12

5.28 De-Moivere’s theorem
x 3 to 9

Day 13

5.29 Roots of a complex number
ex 1 to 3
5.30 Roots of unity
5.31 Cube roots of unity
ex 1 to 7

Day 14

5.32 Logarithm of a complex number
ex 1,2

Day 15
Illustrative Obj type Examples 1 to 15


From Day 16 take it as revision period

Day 16
I.O.T.E. 16 to 25


Day 17
I.O.T.E. 26 to 35

Day 18
I.O.T.E. 36 to 45


Day 19
46 to 55


Day 20
Objective Type Exercises 1 to 10


Day 21
O.T.E. 11 to 20

Day 22
O.T.E. 21 to 30

Day 23
O.T.E. 31 to 40

Day 24
O.T.E. 41 to 50

Day 25
O.T.E. 51 to 60

Day 26
O.T.E. 61 to 80 do only odd numbered problems

Day 27
O.T.E. 81 to 100

Day 28
O.T.E. 101 to 120

Day 29
O.T.E. 121 to 140

Day 30
O.T.E. 141 to 160

Still the book has many many probles. You have to do these problems as a special task and also as a revision whenever you find extra time.