In the last article,we learnt about** iota** which is a** complex number** equal to . Now, can we find power of iota () when n is any whole number. Lets simply calculate some of them and then I will define some general rule.

Now, we can make a general rule which will help us to find power of for any value of integer.

When we carefully look at the above calculations, we can see that

, where n is any whole number. ** (1)**

, where n is any whole number. ** (2)**

, where n is any whole number. ** (3)**

, where n is any whole number. **(4)**

We can explain** (1)**, **(2)**, **(3)** and** (4)** in more simpler words with the help of example.

Suppose, we want to evaluate . Just divide 2001 with 4 and note down the remainder. When we divide 2001 by 4 then we get remainder equal to 1. Therefore, it can be placed in category **(2). **Hence, the answer would be

Lets take another example, we want to evaluate , we just divide 1146 by 4 and we note that the remainder comes out to be equal to 2. It can be placed in **(3) **category. Hence, the answer is equal to -1.

**What you learnt in this article?**

- How to find when n is any whole number.