Question

Evaluate i^5 - i.Where i is a complex number.

Answer 1

i^5 = i^4 * i^1 = 1 * i = i

Answer: i

Answer 2

Is i^5=i ?

Answer 3

yes

Answer 4

There are 4 possisble values as shown in the chart. Then, the powers of i repeat. So, if you were to simplify i to the 27th power. (i^27), then you would realize that after every fourth power of i, the cycle of answers repeats. Then, divide 27 by 4 and look at the remainder. 27/4 = 6 with a remainder of 3.

So, i ^ 27 = i ^ 3 = - i.

What's going on is that i^27 =( i^4) ^6 times i^3 which is (1)^6 times i^3 = 1 times (-i) = -i.

Hope this helps.