The beauty of complex numbers.

 Whenever we think of numbers, the first and foremost thing that comes to our mind is the natural numbers( denoted by N) and the integers(denoted by Z). But what we forget most of the time is that the real beauty lies in the complex numbers, which is ultimately formed as a basis whenever we are studying Linear Algebra, at our undergraduate level. 

Coming to study material, complex numbers can be studied in two different ways, in the form of JEE, where we have to focus on the formulae(obviously after learning the concept) and then solve dozens and dozens of formulae based questions, and the other one is in the form of JEE Advanced and entrances for ISI,CMI,IMA, where the concept is the main crux.

Complex numbers are usually introduced to high-school students in a rather confusing manner. Till a certain grade they are told that the square-root of a negative real number is “forbidden”, and then  is introduced all of a sudden.

The true taste of complex numbers lies in the geometrical approach of it.

According to my knowledge of both JEE and the other entrances, and in accordance of my school teachers and my mentors, I would highly recommend these books---

1. Algebra for JEE Advanced by G.Tewani.

2.Complex Numbers from A to....Z by Titu Andresscu

3.Challenges and Thrills to pre- college mathematics by V Krishnamurthy

If u all are done with these, then u can try out bashing and understand it here-

https://www.youtube.com/watch?v=a0ouhBuCgoY