Definition of complex number

In the previous post we have discussed about 11th Grade Math and In today's session we are going to discuss about  Definition of complex number.

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Here we are going to discuss an important concept that is complex number. Complex number can be defined as any number that can be written in the form of p + iq, here value of ‘p’ and ‘q’ stands for real number and ‘i’ stands for imaginary unit. Here value of ‘i’ is given as √ -1. In above given form ‘p’ is denoted as real part and ‘q’ is denoted as imaginary part of complex number. Complex number p + iq can also be described using the point (p, q). If its real part is given as zero then it is called as pure imaginary and if its imaginary part is zero then it is known as real number. Now we will discuss some rules of complex number.

 i = √ -1, the value of 'i' is represented as √ -1. Here if we use iota symbol in the equations then we can write the square root of negative numbers. For example: (√ x (√ y)), we can also write this given value as √ xy.

Let’s discuss some rules that are used for solve imaginary numbers. As we discussed above value of 'i' is given as √ -1, on squaring the iota we get:

= i² = √ -1 * √ -1, we get the value of i² = -1.

In case of i³ it can also write this equation in squaring form:

= i³ = i² * i; (we know that value of i² is -1).

= -1 * i = -i.

In case of i⁴, first write it in the squaring form,

= i⁴ = i² * i², put the value of i² we get:

= -1 * -1 = 1. This is all about complex number definition.

There are different types of Multiplication Properties which are identity, commutative and so on.

Iit jee syllabus can be downloaded online.