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- Available Batches
- 22 Apr 2021
- 20 Lectures

Description

Complex numbers, like any other class of numbers, are the result of abstract ideas which turned out to be really useful in our daily lives. Indeed, the complex numbers, though with subtle influence for most people, is extremely important in the fields of Science and Engineering.

This course is intended for the online learner who wants to understand the subject starting with basic real numbers Math background. Regardless of the reason you have to learn complex numbers, this course provides easy and step-by-step explanations.

What will you learn?

- You will able to solve problems related to complex number asked in various competitive exams
- You will able to understand all the concepts using in this course
- you will be familiar with complex number and will perform better in various exams
- Students will learn all about Complex Number
- Basic about Complex Numbers
- Cube root of unity
- Geometry in Complex number
- Complex Straight line
- Complex circle
- complex conic section
- nth root of unity

What knowledge and tools are required?

- All the required stationery needed to learn math like pencils, erasers, notebooks, etc.
- Laptop/ Smartphone with a good internet connection
- Learners should know basic maths up to 10th standard and will able to perform maths basic operations
- Students should have a clear knowledge of Basic Mathematics for IIT-JEE and Board exams like Inequality, modulus, interval, number systems

Who should take this course?

- Students of Class 11th and 12th.
- Students at degree level studying mathematics also use this course to improve their subject knowledge
- Students for various Board Exam like- CBSE, ICSE and all other states Board
- Students who want to understand Complex Number completely

Lecture 1 :- Introduction of this Course

In this lecture, we will discuss what exactly we will study throughout this course and how you will prepare for various exams with the next series of lectures.

- Topics

- 1. Syllabus walk through
- 2. preparation tips

Lecture 2 :- Basic about complex number

- Topics

- 1. Imaginary unit
- 2. complex number and their representation
- 3. Real and Imaginary part of complex number

Lecture 3 :- Components of Complex Number

- Topics

- 1. Modulus of complex
- 2. conjugate of complex number
- 3. equality of two complex number

Lecture 4 :- Operation on Complex Number

- Topics

- 1. Operation on Complex Number
- 2. properties of operations
- 3. additive inverse
- 4. multiplicative inverse

Lecture 5 :- Problem discussion

- Topics

- 1. Some problems on basic complex
- 2. geometrical representation of complex number

Lecture 6 :- Arguments of Complex number

- Topics

- 1. principal arguments
- 2. different types of complex numbers
- 3. Arguments related problems

Lecture 7 :- Euler's theorem

- Topics

- 1. Euler's theorem
- 2. polar form of complex number
- 3. Geometrical meaning of conjugate of complex number
- 4. properties of conjugate

Lecture 8 :- Properties of Modulus of complex number

- Topics

- 1. properties of modulus of a complex number
- 2. related examples
- 3. related problems discussion
- 4. related problems discussion

Lecture 9 :- Argument properties

- Topics

- 1. properties of argument of a complex number
- 2. problems based on properties of modulus and arguments
- 3. suitable examples

Lecture 10 :- Demoivre's Theorem 1

- Topics

- 1. Demoivre's Theorem 1 and problems based on this concept.
- 2. related problems discussion

Lecture 11 :- Demoivre's theorem 2

- Topics

- 1. Demoivre's theorem 2
- 2. standard problems related to this theorem

Lecture 12 :- Question Bank solution

- Topics

- 1. Discuss Question asked in various exams AIEEE and IIT
- 2. Mistakes in Computation problem
- 3. questions asked in board exams

Lecture 13 :- Cube Root of Unity

- Topics

- 1. Explanation of Cube root of Unity
- 2. properties of cube root of unity
- 3. important formulas
- 4. problems discussion related to cube root of unity

Lecture 14 :- Square root of a Complex Number

- Topics

- 1. Derivation of formula of square root of complex numbers
- 2. two different methods to find square root of complex number
- 3. related problems discussion

Lecture 15 :- Geometry in Complex Number

- Topics

- 1. Some standard points of triangle in complex form
- 2. Centriod of trinagles
- 3. orthocentre, circumcentre and incentre of triangles in complex form
- 4. problem based on equilateral triangles

Lecture 16 :- Rotation theorem

- Topics

- 1. Rotation Theorem of Complex number
- 2. examples related to rotation theorem
- 3. related problems discussion
- 4. Multiplication of a Vector with exp(i theta or -i* theta)

Lecture 17 :- Straight lines in Complex Number

- Topics

- 1. Angle between two line segment in term of Argument
- 2. Reduction of equation from Cartesian to Complex Form and Vice-versa
- 3. General Equation of Complex Straight line in Complex Form
- 4. Real Slope of Complex Straight Line
- 5. Equation of Complex Straight Line in Parametric form
- 6. Equation of Complex Straight Line in Determinant Format
- 7. Co-linearity of Three Given Points
- 8. Equation of Parallel or Perpendicular Line to a given Line
- 9. Length of Perpendicular of a point from a Complex Straight Line
- 10. Complex Slope of Straight line
- 11. Relation Between Real slope and Complex Slope
- 12. Condition of Parallelism/Perpendicularity in term of Complex Slope
- 13. Equation of Perpendicular Bisector in Complex Form
- 14. related problems discussion

Lecture 18 :- Complex Circle

- Topics

- 1. General Equation of Complex Circle in form of complex Number
- 2. Standard Equation of Complex Circle
- 3. Equation of Complex Circle for given extremities of Diameter
- 4. Condition for Four points to be Con-cyclic in Complex Form
- 5. Equation of Complex Circle passing through three given points
- 6. Equation of a Tangent to the Complex Circle

Lecture 19 :- Conic section in Complex form

- Topics

- 1. Equation of Parabola in Complex Number
- 2. Equation of Ellipse in Complex number
- 3. Equation of Hyperbola in Complex Number
- 4. related problems discussion

Lecture 20 :- Question Bank discussion of Complex number

- Topics

- 1. question asked in JEE mains exam
- 2. questions asked in JEE Advanced exams
- 3. Problems asked in board exams

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Instructor Profile

**Skills: **

Persuing Batchelor of Technology from Indian Institute of Technology Dhanbad, Jharkhand India. Math class was always so frustrating. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!” So I started tutoring to keep others out of that aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. I love to teach mathematics through my unique method of explanation.

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