2007-12-20 08:45:28 · 7 answers · asked by Latoya G 1 in Science & Mathematics ➔ Mathematics
i ^(2x) = - 1 where 2x is an even power
Thus
i^(102) = - 1 where 102 is an even power
2007-12-20 09:17:51 · answer #1 · answered by Como 7 · 3⤊ 0⤋
Greetings,
i^1 = i
i^2 = -1
i^3 = - i
i^4 = 1
i^5 = i
i^6 = -1
The pattern of i, -1, -i , 1 repeats with a period of 4, and by looking at the remainder after dividing by 4, we can see which of the 4 values it will be
So 102/4 = 25 remainder 2 which gives the same value as i^2 or -1
i^102 = -1
Regards
2007-12-20 16:51:38 · answer #2 · answered by ubiquitous_phi 7 · 2⤊ 1⤋
-1.
i to the power of 1 is i.
i to the power of 2 is -1.
i to the power of 3 is -i
i to the power of 4 is 1
This series will repeat (modulo 4). 102 is even, but not divisible by 4, so it is the same as i^2 = -1.
2007-12-20 16:52:41 · answer #3 · answered by MVB 6 · 1⤊ 1⤋
i^102 = i^100*i^2 = (i^4)^25*(--1) = 1*(--1) = -- 1
2007-12-20 16:54:07 · answer #4 · answered by sv 7 · 1⤊ 1⤋
-1
i^2 = -1
i^102= i^2^50 x i^2 = 1 x -1 = -1
2007-12-20 16:51:22 · answer #5 · answered by pjpudge1414 2 · 2⤊ 1⤋
i^102 = (i^2)^51 = (-1)^51 = -1
2007-12-20 16:57:40 · answer #6 · answered by Christophe G 4 · 1⤊ 2⤋
any even exponent will give you -1
2007-12-20 16:51:39 · answer #7 · answered by Joe L 5 · 0⤊ 7⤋