last question finally
simplify complex numbers:
i^16/i^3
Since you are dividing two expressions with the same base, you can just subtract the exponents:
i^(16-3) = i^13
And since i = (-1)^(1/2), any i to an even power will yield -1. So:
i^12 * i^1 = (-1) * i = -i
i^13, since you subtract 3 from 16.
thanks
To simplify the expression (i^16) / (i^3), you need to understand the properties of exponents and complex numbers.
First, let's simplify the numerator (i^16):
The imaginary unit i follows a pattern where it repeats every 4 exponentiations. i raised to the power of 1 gives i, i^2 gives -1, and i^3 gives -i. Since i^4 equals 1, we can use this pattern to simplify i^16.
i^16 can be broken down as follows:
i^16 = (i^4)^4 = (1)^4 = 1
Now, let's simplify the denominator (i^3):
As mentioned earlier, i^3 equals -i.
So, the expression (i^16) / (i^3) can be simplified to:
1 / (-i)
To further simplify this, we multiply the numerator and denominator by -i:
(1 / (-i)) * (-i / -i) = -i / (-i * -i) = -i / 1 = -i
Therefore, (i^16) / (i^3) simplifies to -i.