how to simplify: i^32,530
2006-11-06 07:16:50 · 2 answers · asked by brunette 1 in Education & Reference ➔ Homework Help
It is -1.
To figure this out, follow the pattern of i, as you raise it to various powers:
i^1 = i
i^2 = i*i = -1
i^3 = i^2*i = -1 * i = -i
i^4 = i^3 * i = -i * i = -(i*i) = -(-1) = 1
i^5 = i^4 * i = 1 * i
etc.
So, you can see that the powers of i depend on what it is modulo 4.
You can see that i^32,530 can be written as i^2, since 32530/4 yields a remainder of 2. Thus, you know that i^32,530 = i^2 = -1.
2006-11-06 07:25:53 · answer #1 · answered by Rev Kev 5 · 0⤊ 0⤋
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
The above repeats iyself over and over.
S0 divide 32,530 by 4 and get 8,132 with a remainder of 2. this says you went through the above repeating series 8,132 times and are now on the second term in the series which is -1.
The answer is -1
2006-11-06 15:37:02 · answer #2 · answered by ironduke8159 7 · 1⤊ 0⤋