Complex Numbers - Basics | Don't Memorise

Complex Numbers - Basics | Don't Memorise

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Language: English

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00:03
In the previous videos, we learnt that it is possible to have square root of a negative number, but it involved using a new number 'i', which is equal to the square root of negative 1. These numbers are called imaginary numbers and could be of the form 'bi' where 'b' is a real number. And 'i' is equal square root of negative 1. Numbers like 'i', '2i', 'negative 4i' are all imaginary numbers! What if we have a number like 3 plus 7i ? Will this be an imaginary number? Well, we can be sure that this part of the number is imaginary. And this part is a real number. So this is a mix of real and imaginary parts. And this is what we call an example of a complex number. Real plus imaginary gives us a complex number. It's of the form 'a' plus 'bi' where 'a' and 'b' are real numbers, and 'i' is the unit imaginary number. Now let's play around with this basic form.
01:08
Observe that when 'a' is equal to '0', what is left will be an imaginary number. And when 'b' is equal to '0' we only have a real number. So what are the real and imaginary parts, in the basic form of a complex number? 'a' is called the real part and 'bi' is called the imaginary part. Now let me ask you something interesting! When will the two complex numbers 'a' plus 'bi' and 'c' plus 'di' be equal? They will be equal only if both the conditions are satisfied. First 'a' is equal to 'c' and second 'b' is equal to 'd'. Yes, only if 'a is equal to c' and 'b is equal to d' will the two complex numbers be equal. Real parts equal and the imaginary parts as well are equal. However, the real numbers are comprehensible. Why are we moving towards complex numbers? Do they lead to anything worthwhile? There were doubts about it. Even among mathematicians who initially developed this concept.
02:21
While some did not believe in them. Others were desperately trying to prove their existence. Still the journey continued and complex numbers were finally allowed by mathematicians. Today, the most people may find complex numbers incomprehensible or difficult to understand. They do exist in some form and serve the purpose of understanding of nature. Engineers use it to study stresses on beams, phenomena of resonance and the flow of fluid around objects, such as water around a pipe. They make it easy to understand the flow of current through electronic circuits, using resistances, inductance and capacitors. They are also used in electromagnetism, where rather than trying to describe an electromagnetic field by two real quantities separately. They are described as a single complex number, of which electric and magnetic components are simply the real and imaginary parts. How exactly are they used here?
03:24
Well, it's an advanced topic which we will cover in a graduation level math videos.

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