Numbers which contain iota are known as imaginary Numbers. Generally representation of Imaginary Number
is given by symbol 'i'. There are some rules are for complex imaginary numbers which are given below:
In mathematics the value of 'i' is given by: i = √-1, on squaring iota we get:
= i2 = √-1 *√-1, on solving we get value of i2 is -1.
In case of i3 we can also write this in squaring form:
= i3 = i2 * I; ( we know that the value of i2 is -1).
= -1 * I = -i.
In case of i4, first write it in Square form,
= i4 = i2 * i2, put the value of i2 we get:
= -1 * -1 = 1. These are some basic rules of imaginary numbers.
Simplifying square root of (-16), according to above rule we can write it as:
= √-16 = √ 16.(-1) we can also write it as:
=√16.√-1 = √16 . i = 4i,
Suppose an expression (i) (3i) (4i) and we have to solve the given expression.
To solve this expression we have to follow some steps which are shown below:
Step 1: To solve this fraction first of all we will multiply the first value with second value and then result we will get is multiplied by third value.
= (i) (3i) (4i);
On multiplying we get:
= (3i2) (4i);
On further multiplying we get.
= 12i3, (we know that value of i2 is -1, so we can also write this given expression as):
= 12 i * i2,
= 12 * i * (-1);
This is how we can solve complex imaginary numbers.