##### Like what you saw?

##### Create FREE Account and:

- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- FREE study tips and eBooks on various topics

# Powers of i - Problem 2

###### Carl Horowitz

###### Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Simplifying i to a power. In this problem what we’re looking at is i to the negative 273 and there’s a couple of things that we need to take into consideration to begin with.

We know that a negative exponent puts the number in the bottom. So the first I want to do is rewrite this as 1 over i to the 273.

Next thing I want to do is actually simplify whatever i to the 273 is and in order to do that I want to find the nearest multiple of 4 that’s close to 273. In order to do that, we just do division; how many times does 4 go into 273? 4 into 27, 6, 24, 33 4 into 33 gives us 8, 32, subtract so I know I have a remainder of 1. This corresponds to i to the first which tells me I just have an i, sorry, that this statement i to the 273 is the same things as i to the first. Wow I can’t write today, i to the first which is just i. So I have one over i.

We still have an i in the denominator which we’re not allowed to do. So what is till have to do is rationalize this fraction. In order to get rid of i I need to multiply by i over i, end up with i over i², i² is the same thing as -1 so what I end up with is i over -1 or, -i.

Whenever we’re dealing with i to a negative power the process is the same as dealing with a positive power in terms of finding out what that term is but we still may have to rationalize our denominator when we’re finished.

Please enter your name.

Are you sure you want to delete this comment?

###### Carl Horowitz

B.S. in Mathematics University of Michigan

He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his step-by-step explanations are easy to follow.

i love you you are the best, ive spent 3 hours trying to understand probability and this is making sense now finally”

BRIGHTSTORM IS A REVOLUTION !!!”

because of you i ve got a 100/100 in my test thanks”

##### Concept (1)

##### Sample Problems (2)

Need help with a problem?

Watch expert teachers solve similar problems.

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete