let i = the square root of -1 with i to the 1st power =i, i to the 2nd power= -1, i to the 3rd power =-i , i to the 4th power=1 find ito the power 215
i^215 = i^212*i^3 = i^3 = -i
(i^212 = 1 because 212 is evenly divisible by 4)
In other words,
i^212 = (i^4)^53 = 1^53 = 1
To find i to the power of 215, we need to determine the pattern that i follows when raised to different powers.
We know that i to the 1st power is equal to i (i^1 = i).
i to the 2nd power is equal to -1 (i^2 = -1).
i to the 3rd power is equal to -i (i^3 = -i).
i to the 4th power is equal to 1 (i^4 = 1).
We can see that the powers of i repeat every 4 terms. So, i^5 is the same as i^1, i^6 is the same as i^2, and so on. Therefore, i to any power that is divisible by 4 will always be equal to 1.
Now, let's calculate i to the power 215:
Since 215 is not divisible by 4, we need to find the remainder when 215 is divided by 4. The remainder is 3.
Thus, i to the power 215 will be the same as i to the power 3.
We know that i^3 is equal to -i.
Therefore, i^215 is equal to -i.
So, i to the power 215 is -i.