SOLUTION: what is i to the 235th power

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:

Answer:

RELATED QUESTIONS
what is i to the 50th power? (answered by rfer)
what is 'i' to the 233... (answered by stanbon)
what is i to the 27th... (answered by ewatrrr)
what is i-100? i to the -100... (answered by Alan3354)
what is i to the 16th power? What is i to the 255th power? What is i to the 5692nd... (answered by fractalier)
what is i to the third power and... (answered by solver91311)
what is the greatest common factor of 28x to fourth power and 35x to sixth power I... (answered by mananth)
WHAT IS THE ANSWER IF I EVALUATE 6 TO THE 2ND POWER AND ALSO8 TOTHE 2ND POWER AND ALSO4... (answered by xshorty73)
what is: i squared i cubed and i to the fourth... (answered by longjonsilver)