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The Basics of Learning Complex Numbers and the Identities

Complex Numbers

In Mathematics students have to handle multiple types of numbers. Not all of them are whole or real like ‘4’, ‘9’, etc. Some of them may not even have a proper definition. If you speak logically these numbers are not supposed to exist. Yet scientists need them to solve equations at higher stages. Such complex numbers have a specific structure divided into two parts. One of them is like the normal numbers that you use. The other part is imaginary and can be represented as a multiple of root (-1). When you fuse these two parts, you get the entire number.

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Components present in a Complex Number

There are two main components known as the real and imaginary. The first one includes all types of numbers that you use in Mathematics. Be it negative, decimal, fraction, etc. But the value that you get has a proper definition. The latter part of a complex number seems to have no existence. You cannot say what the value of root of -1 is. The root of negative numbers cannot be depicted or calculated. But if you take that part as ‘i’ you get a co-efficient as well. Thus, whenever you have to represent the imaginary number, take the ‘i’ common and you will get the value.

The Process of Absolute Value

You can represent complex numbers in different forms. After a stage, the question may ask you to draw the graph of the complex form. However, it is possible to find the absolute value of any complex number you have. It is a simple process if you understand it well. First, you have to simplify the entire equation. In usual cases, the examiner will not give you the complex number directly. You will have to derive it after treating it like normal equations. Keep the real as well as the imaginary part separate. Once you get that, take squares of both and sum them together. Find the square root of this result and you will know what the absolute value is.

How to do Operations?

There is not much difference when it comes to all the arithmetic operations. You can just treat the two sections separately here. For example, if you want to add, on one side take all the real numbers. Then once you get the answer for this, that will be the real value of your final solution. For the imaginary section, you need to take the ‘i’ outside the bracket. Then you can do the addition in the same way and get your final imaginary solution. For multiplication, you can use the process of algebra. Just remember that when you multiply ‘i’ with ‘i’, you get one. The simple reason is that when you do the square, the root will become extinct.

In division, it is necessary to find the conjugate version as well for the students. Only then you can apply the other methods and find the final value. Besides these, certain identities can help you with the sums. Some of them obey the same rules that you see with other numbers. One of them is that when you take the product of two complex integers, the answer is real.

The Main Importance of this Topic as a Whole

The topic of complex numbers has a lot of relevance in quantum mechanics. You can treat them as a two-dimensional vector as well. If you plot a graph it will have separate values for the two axes. In the chapter on the interference of light, you will see the effect of complex numbers. In case you are new to the topic, find out relevant information from the reputed Cuemath website.

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