Question:

when simplified, i^27 + i^34 is equal to?
^(exponent) (1)i (2)i^61 (3) -i - 1 (4) i - 1

Answers:

A-Best: Powers of i repeat every four times. i = i i^2 = -1 i^3 = -i i^4 = 1 After that everything repeats. Take each exponent and divide by 4 and pay attention to the remainder. 27 divided by 4 is 6 with a remainder of 3, so i^27 = i^3 = -i 34 divided by 4 is 8 with a remainder of 2, so i^34 = i^2 = -1 Answer: -i - 1  

A: Zero  

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A: i^27 + i^34 = i^61  

A: There are only 4 powers of i. we have i^1 = i, i^2 = -1, i^3 = -i and i^4 = 1. Now break down the powers you have. i^27 = (i^3)^9 = (-i)^9 = -(i^9) (odd power) = -i and i^34 = (i^2)^17 = (-1)^(17) = -1 since it's an odd power.  

A: (3) -i - 1  

A: i^27=i i^34=-1 i^61=i -i-1=-i-1 i-1=i-1 I think I caught all of those.  

A: i^0 = 1 i^1 = i i^2 = -1 i^3 = -i i^4 = 1 (And now it repeats) Therefore, if we divide the exponent by 4, the remainder will tell us which to use. For example, i^5 = i^1 = i, because the remainder when 5 is divided by 4 is 1. When 27 is divided by 4, the remainder is 3. This means that i^27 = i^3 = -i. When 34 is divided by 4, the remainder is 2. This means that i^34 = i^2 = -1. So the expression i^27 + i^34 is the same as -i - 1, which is answer 3.  

A: i^27 + i^34= [(i^4)^6]*(i^3) + [(i^4)^8]*(i^2) =[1]*[-i]+[1]*[-1] = -1-i  

A: i^27 = i^3 27 / 4 = 6 and reminder 3 = - i i^34 = i^ 2 34 / 4 = 8 and reminder 2 = -1 so i^27 + i^34 = -i -1 notice : i = sqroot( -1 ) i^2 = -1 i^3 = - i i^4 = 1  

A: i^1 = i i^2 = -1, i^3 = -i i^4 = 1 i^5 = i^4 * i = 1*i It goes in a cycle i, -1, -i, 1, i, -1, and so on Every exponent that is a multiple of 4(4,8,12, 16,20, and so on) results in 1 If the exponent is one less than a multiple of four as in i^27, you get -i. If the exponent is even but not a multiple of four, -1. If the exponent is three less than a multiple of four, or 1 more than a multiple of four, i. Look at the exponents first, then the addition.