How do you simplify i38?
i38 = 38 @ 90 deg.
To simplify the expression i^38, we need to know the properties of the imaginary unit.
The imaginary unit, denoted by "i," is defined as the square root of -1. It has the property that i^2 equals -1.
To simplify any expression involving i, we use the property that i^4 is equal to 1. This means that after every fourth power, the powers of i repeat.
So, let's simplify i^38 using this property:
i^38 = i^(4 * 9 + 2)
Since the power of i is raised to a multiple of 4 (4 * 9) plus 2 (i^2), we can rewrite the expression as:
i^38 = (i^4)^9 * i^2
Since i^4 equals 1, we have:
i^38 = 1^9 * i^2
Simplifying further:
i^38 = 1 * i^2
Finally, using the property that i^2 equals -1:
i^38 = 1 * -1
The simplified expression is:
i^38 = -1