In mathematics, you might have heard about various types of numbers such as real numbers, natural numbers, whole numbers, imaginary numbers, and various others. Likewise, a complex number is a type of number which is represented in the way of, a+ib where a and b are regarded as the real numbers and i is defined as an imaginary number which is also known as ‘iota’. Let us take an example so that you understand complex numbers in a better way, ‘4+2i’ is a complex number, where 4 is the real number and 2i is regarded as the imaginary number. In this article, we will try to understand some basic concepts related to complex numbers such as properties of complex numbers, comparison between complex, real, and imaginary numbers, and do a detailed analysis about them.
Some Important Properties of Complex Numbers
From the paragraphs mentioned above, you might have understood the basic concept of complex numbers. These numbers are the numbers that can be expressed in the form of ‘a+ib’ where a and b are the real numbers and ‘i’ is considered as an imaginary number. Like every other number, a complex number also possesses some significant properties. The following points mentioned below analyses the important properties of complex numbers.
- When any two conjugate numbers which are complex in nature are added, the resultant value always comes as a real number.
- Similarly, when any two conjugate numbers are multiplied, the resultant value will also come as a real number.
- Whenever we talk about complex numbers, we should not forget about the associative and commutative law of addition and multiplication as both of these laws are obeyed by a complex number.
- If you multiply two complex numbers, there resultant value will form a conjugate number which should be positive in nature.
Complex Numbers Vs Real Numbers Vs Imaginary Numbers
Complex Numbers: It is a type of number which is represented in the way of, a+ib where a and b are regarded as the real numbers and i is defined as an imaginary number which is also known as ‘iota’. For example, ‘4+2i’ is a complex number, where 4 is the real number and 2i is regarded as the imaginary number.
Real Numbers: The combination or collection of both rational numbers and irrational numbers is known as real numbers. Some examples of real numbers are as follows; 32, -14, 6.99, 22/7, 3.14, etc.
Imaginary Numbers: An imaginary number is a part of a complex number where the imaginary number gets multiplied by the real number to form a complex number. It is also known as ‘iota’. For example, if 4+2i is a complex number, here 2i is regarded as an imaginary number.
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