2007-11-05 03:38:34 · 5 answers · asked by Deannapril H 1 in Science & Mathematics ➔ Mathematics
i^n = i^(n mod 4)
This means that for any power (n) of the imaginary number i, the expression (i to the n) is equal to (i to the (remainder of n divided by four)).
i^41 = i^(41 mod 4)
41 mod 4 = remainder of 41 / 4 = 1
i^41 = i^1 = i
2007-11-05 03:52:56 · answer #1 · answered by marbledog 6 · 0⤊ 0⤋
Since i² = -1, i^4 = 1, so
i^41 = (i^4)^10 * i
= 1^10 * i = i.
2007-11-05 11:54:35 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
i^1 = sqrt(-1) = i
i^2 = sqrt(-1)^2 = -1
i^3 = sqrt(-1)^3 = -i
i^4 = sqrt(-1)^4 = -1*-1 = 1
41 = (4*10)+1
i^40 = 1
i^41 = i
2007-11-05 11:48:14 · answer #3 · answered by Grant d 4 · 1⤊ 0⤋
In electrical engineering we used j for sqrt(-1). i was reserved as the symbol for current (amps).
So I can't answer because no value for i was given.....lol
2007-11-05 12:09:52 · answer #4 · answered by andyg77 7 · 0⤊ 1⤋
The answer is i.
2007-11-05 11:46:13 · answer #5 · answered by kaejer1 3 · 0⤊ 0⤋