Answer :
i is the square root of -1. It is an imaginary number because you can't find the answer to the square root of a negative number.
However, the (square root of a number) squared is that number, for example sqrt4 * sqrt4 = 4.
Likewise, sqrt(i) * sqrt(i) = -1. You can see it as sqrt(-1) * sqrt(-1) = -1.
If you multiply by another sqrt(i) however, sqrt(i)^3, then the last sqrt(i) will be left and there will still be an imaginary number. You will have -1 * i, which is -i.
However, if you have sqrt(i)^4, then you have sqrt(-1)*sqrt(-1)*sqrt(-1)*sqrt(-1), which is -1*-1, which equals 1. You see that pairs of sqrt(i)'s balance and take out imaginary numbers.
So, sqrt(i) to odd powers will still have imaginary numbers, while sqrt(i) to even powers won't have imaginary numbers.
However, the (square root of a number) squared is that number, for example sqrt4 * sqrt4 = 4.
Likewise, sqrt(i) * sqrt(i) = -1. You can see it as sqrt(-1) * sqrt(-1) = -1.
If you multiply by another sqrt(i) however, sqrt(i)^3, then the last sqrt(i) will be left and there will still be an imaginary number. You will have -1 * i, which is -i.
However, if you have sqrt(i)^4, then you have sqrt(-1)*sqrt(-1)*sqrt(-1)*sqrt(-1), which is -1*-1, which equals 1. You see that pairs of sqrt(i)'s balance and take out imaginary numbers.
So, sqrt(i) to odd powers will still have imaginary numbers, while sqrt(i) to even powers won't have imaginary numbers.
Answer:
-1
Step-by-step explanation:
If i is raised to an odd power, then it can not simplify to be?
-1
-i
i
Odyssey