Question 426015: I am taking a placement test next week and i need some help with some math.
with complex numbers i^32 power Found 2 solutions by josmiceli, solver91311:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Each time you multiply a number by , you
rotate 90 degrees in the complex plane.
You start at
i^0 = 0 degrees = (+) real numbers
i^1 = 90 degrees = (+) imaginary
i^2 = 180 degrees = (-) reals
i^3 = 270 degrees = (-) imaginary
i^4 = 360 degrees = back to (+) reals
--------------------------
Note that is a complete rotation back to
0 degrees
Divide by
This is 8 times around back to 0 degrees with no remainder,
so
Remember back when you first learned to divide and you would have an answer that was composed of a quotient and a remainder, such as 10 divided by 3 is quotient 3 remainder 1. This is called integer division, and there is a special function called the "mod" (short for modulo) function that is the remainder when one integer divides another. Using our 10 divided by 3 example, 10 mod 3 = 1
Anything to the zero power is 1, and anything to the 1 power is itself. And also remember . With that in mind, consider the following facts:
Definition of
and the pattern repeats...
That means that
John
My calculator said it, I believe it, that settles it
