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.