A Mathactive Educator, Lover of books, Avid learner, Online Tutor, Founder of Mathemission. 

Ashutosh Kumar

This course covers the topic Complex Numbers which will stand helpful for the students studying in grade 11 and also for JEE aspirants. Moreover,  Undergraduate students looking for the foundation of Complex Analysis can also get help from this course.

IIT JEE 2020 and 2021 Main and Advanced exam preparation. Know about detailed syllabus, best books, exam pattern and dates. Cover previous year question papers and book solutions from great educators.

IIT JEE

JEE Main and Advanced Preparation

English

A Course on Complex Numbers

Complex Numbers

Algebra

Mathematics

IITJEE, NEET UG and Foundation

Ace the toughest competitive and government exams in India 

Test Preparation

This is the introductory lesson on Complex Numbers where concept of imaginary unit is covered. Starting from the origin of imaginary unit, that we call iota, we see some examples on its property.

Lesson 1: Introduction to Imaginary Unit

In this lesson we will see the definition of a compex number, it's conjugate and it's properties followed by some examples.

Lesson 2: Complex Number and its Conjugate

This lesson contains the modulus of complex number and it's properties followed by an example.

Lesson 3: Modulus of a Complex Number

In this lesson we will learn the Geometrical representation of a compex number. What will happen when iota is multiplied to a complex number? We shall see some Geometrical aspects of through the and of this question. 
One little Correction: In Column match problem the option (e)  in the column B should be (i^2 z) instead of (i^3 z). I hope students can take it as a human error.

Lesson 4: Geometrical Representation of a Complex Number

In this lesson argument of a complex number is discussed with examples.

Lesson 5: Argument of a Complex Number

This lesson covers the properties of argument followed by some examples.

Lesson 6: Properties of Argument

This is the seventh lesson in which we see the 'Polar form of a complex number' followed by an important example.

Lesson 7: Polar Form of a Complex Number

This lesson covers the 'Euler form of complex number and Demoivre Theorem. We also see the applications of these through some examples.

Lesson 8:Euler Form and Demoivre's Theorem

This lesson conveys the geometrical aspects of Sum, Difference, Product and ration of give two complex numbers. As this lesson doesn't have any examples in it, only curious students are requested to go through it.

Lesson 9: Operations on Complex Numbers

In this lesson some important properties involving conjugate and modulus are discussed with their proofs. Students are suggested to try the proofs by their own also.

Lesson 10: Properties Involving Conjugate and Modulus

Triangle Inequalities are important tools to solve the problems in which Max an Min are are asked. Let's watch how we can apply.

Lesson 11: Triangle Inequality and its Application

We can treat two complex numbers as two points in a plane. The idea of the the length segment can be applied to solve the problems in a smart way. Let's watch.

Lesson 12 : Distance between two Complex Numbers (Line Segment).

The distance between two Complex Numbers can also be interpreted as circle with given centre. Let us see how.

Lesson 13: Distance between two Complex Numbers (Circle).

If two complex numbers are placed in a complex plane, we can find the slope of the line segment joining these. And so, we can have angle between two different such line segments. What are the consequences then? Let's see.

Lesson 14: Angle Between two line segments.

Problem solving skills are developed only when we really face the problems. There is no unique set of algorithms or steps of strategy by which we can learn Mathematics. Just follow the basics and fight with problems. You will be victorious.

Lesson 15: Problem Solving Skills (Part one)

We are learning  problems solving skills through solving the problems only. This lesson is also containing some problems with their solutions discussed.

Lesson 16: Problems Solving Skills ( Part Two).

Part 3 also contains some problems discussed with their solutions. Most of the problems are taken from JEE advanced Papers of different years.

Lesson 17: Problems Solving Skills (Part Three).

The lesson, once again discusses the problems and their solutions. One suggestion- Please watch lesson 14 before this.

Lesson 18: Problems Solving Skills ( Part Four)

In this last lesson on problems solving skills, we shall discuss two problems asked in JEE.

Lesson 19: Problems Solving Skills (Part Five)

There are various ways to find the square root of a complex number. Here, we will derive a handy formula to find the square root. Let's do that.

Lesson 20: Square Root of a Complex Number.

This lesson covers the concept of cube roots of unity, their geometrical interpretation and some examples.

Lesson 21: Cube Roots of Unity

Let's do some problems on the concept of cube roots of unity.

Lesson 22: Some Problems on Cube Roots of Unity.

Here, we shall learn the concept of the nth roots of unity. We can observe that cube roots of unity is one of the particular case of this general version.

Lesson 23: The nth Roots of Unity

Let's solve some problems on the nth roots of unity.

Lesson 24: Some Problems on the nth Roots of Unity.

Complex roots of a quadratic equation can be found by using quadrratic formula. What kinds of questions we may be asked if one of the complex roots is known for any given equation? Let's see.

Lesson 25: Equations with Complex Roots.

Here we will see how the equation a straight line in a complex plane can be written.

Lesson 26: Complex Number in Co-ordinate Geometry (St. Line)

This lesson covers circle in a complex plane.

Lesson 27: Complex Numbers in Co- ordinate Geometry (Circle).

In this very short lesson, we will see how the equation ofa parabola can be written in complex number 'format.'

Lesson 28: Complex Numbers in Co-ordinate Geometry (Parabola).

Finally the course got completed with lesson. Thanks for watching.

Lesso 29: Complex Numbers in Co- ordinate Geometry (Ellipse).

A Game Changer in Mathematics, produced multiple 100 percentilers, Air 33 & 34 (Main 2024), his courses are the Benchmark for IIT JEE 

Vineet Loomba

In this course VL Sir will cover all the topics on matrices and determinants from basic to JEE Advanced Level. This course will comprehensively cover the whole syllabus of JEE Main, JEE Advanced, BITSAT, CBSE and State Boards, WBJEE, VITEEE etc.

(Hindi) Matrices Determinants (Zero to Hero) for JEE Main and Advanced : IIT JEE

This course comprehensively covers the complete syllabus of Complex Numbers for JEE Main and Advanced, BITSAT, VIT, CBSE and other regional Engineering Entrance Exams

(Hindi) Complex Numbers (Detailed Course)

IIT Bombay | Taught AIR 1, 6, 20*in JEE Advanced | Taught AIR 28 (AIIMS Delhi) | Tutored INCHO AIR 60 | Mentored multiple 100 percentiles.

Sachin Rana

This course deals with all the important concepts and questions in the chapter Complex Numbers for JEE Main, JEE Advanced, BITSAT, CET and all state engineering exams.

Complex Numbers for IIT JEE

20+ years of Experience in Teaching Mathematics. Mentored 50,000+ students. Produced 100/100 score in Maths.


Vishal Mahajan

In this course, the educator is discussing Complex Numbers & Quadratic Equations for IIT JEE & CLASS 11

(Hindi) IIT JEE: Complex Numbers and Quadratic Equations

I have passed Class 10th and 12th with distinction Marks and currently I am doing Engineering with Computer Science.

Sriram Singh

In this course we will discuss:
The real number system,
Modulus of a real and imaginary number,
algebra, 
conjugate, 
modulus,
argument, 
polar form, 
Root of unity,
Geometrical application,
Various form,
Logarithm of complex number.

(Hindi) Complex Number : IIT JEE

This course is the continuation of the Quadratic Equations(Part I). So, kindly make sure that you've watched the whole Part I before watching this course.

Lessons

29 lessons • 6h 27m

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Lesson 1: Introduction to Imaginary Unit

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Lesson 2: Complex Number and its Conjugate

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Lesson 3: Modulus of a Complex Number

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Lesson 4: Geometrical Representation of a Complex Number

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Lesson 5: Argument of a Complex Number

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Lesson 6: Properties of Argument

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Lesson 7: Polar Form of a Complex Number

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Lesson 8:Euler Form and Demoivre's Theorem

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Lesson 9: Operations on Complex Numbers

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Lesson 10: Properties Involving Conjugate and Modulus

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