Question

Simplify i72

i

–1

–i

1

Answer 1

Firstly tell me when you divide 72 by 4 then what is the remainder??

Answer 2

18

Answer 3

I am asking for Remainder and not quotient..

Answer 4

So, if

Remainder = 0, then answer will be 1
Remainder = 1, then answer will be i
Remainder = 2, then answer will be -1
Remainder = 3, then answer will be -i

Now tell me what is the remainder when you divide 72 by 4??

Answer 5

ohh i see i just figured out the problem i^72 = (i²)^36 = (-1)^36 = 1

Answer 6

You can do this way also..

Answer 7

I suggest you other method:

\[i^4 = 1\]

\[= (i^4)^{18}\]
\(= 1\)

Answer 8

In this case when you divide 72 by 4 you get remainder = 0, so apply the first condition I have written there..