Question 26756: what is i to the 235th power
Found 2 solutions by whty89, bmauger:
Answer by whty89(20)   (Show Source):
You can put this solution on YOUR website! to solve this you need to know the 4 basic powers of i.
i^1=square root of -1=i
i^2=-1
i^3=-i
i^4=1
to find i to any power you just take that number and divide it by 4.
in this case 235/4=58.75
Forget about the whole number, just look at the decimal if the decimal was
.25=i
.50=-1
.75=-i
no remainder equals 1
Answer by bmauger(101) (Show Source):
You can put this solution on YOUR website! i, the imaginary square root of -1, follows a pattern when you raise it to various powers.
By definition any number (even this imaginary one) to the 0th power is 1, so:
Since any number raised to 1 is itself, we start with:
by the definition of i, squaring it gives -1:
taking it to the third power is the same as multiplying -1 (i squared) times i:
and taking it to the forth power is the same as multiplying -1 (i squared) times -1 (i squared):
If we multiply this by another i, i raised to the fifth, we start to see the pattern:
In fact, knowing that i^4=1 means that we can multiply as many i^4 as possible together and still get 1. Example:
Dividing 235 by 4, we get 58.75 so we have a total of 58 4's we can "cancel". Therefore, in your problem, i^235, we can rewrite 235 as 4*58 + 3. Using laws of exponents i to the 235th can be rewritten as:
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