Simplifying Imaginary Numbers with Large Exponents

You may learn imaginary numbers in Algebra 1, Algebra 2, or College Algebra. Many students can be intimidated by these. (“What the heck is an imaginary number?”) But, fear not, they’re not too bad! Today we’ll be looking at simplifying imaginary numbers with large exponents. By learning one simple strategy, you’ll be very comfortable with simplifying any imaginary number.

In the video, I explain how to simplify imaginary numbers with large exponents. This technique makes simplifying imaginary numbers easy to learn. We’ll be using the fact that i^2 = -1. This is our simplifying superpower! First we’ll go over a few small exponents to get the hang of it, making sure we really understand the concept. Then, using our newfound knowledge, we’ll do 4 problems with large exponents. After this, you’ll be comfortable simplifying any imaginary number with a large exponent!

Find the video above or on YouTube.

So, take five minutes to watch, and you’ll be a pro! Then remember to share the love and knowledge with a classmate who could benefit. After that, if you need more help with math from a tutor, head over here for some recommendations.

Leave me a comment below and let me know how your journey with simplifying imaginary numbers is going. Do you have any questions? Or perhaps there is something else you want to learn, either on this topic or another? I’m always looking for recommendations for my next video. Above all, remember that you’re doing great!

-Katie, the online math tutor

Order of Operations: Using PEMDAS to Simplify Expressions

Order of Operations: Using PEMDAS to Simplify Expressions

Using the order of operations (PEMDAS) is a very important skill for any math student starting in pre-algebra. Take the time to learn this skill well since you’ll be using it in nearly every math problem you do!

PEMDAS tells us the order in which to simplify an expression. There are four steps.

  1. Parentheses — this includes all grouping symbols such as brackets and absolute value.
  2. Exponents
  3. Multiplication and Division — do these from left to right.
  4. Addition and Subtraction — also do these from left to right.

In the video I explain how the order of operations works, why we use it, and go over four helpful examples. Take a look for yourself, or share it with a classmate who could benefit.

-Katie, the online math tutor

Binomial Expansion Using Pascal’s Triangle

Binomial Expansion Using Pascal’s Triangle

As an online math tutor, I love teaching my students helpful shortcuts! Algebra 2 and Precalculus students, this one is for you. Let’s learn a binomial expansion shortcut. Let’s say we want to expand (x+2)^3.

Without knowing a shortcut, we would start out by first writing this as (x+2)(x+2)(x+2). Then we could FOIL the first two terms.

(x+2)^3
=(x+2)(x+2)(x+2)
=(x^2+4x+4)(x+2)

Which gets us closer, but now we need to multiply these together (by multiplying everything in the first polynomial by everything in the second polynomial).

=(x^2+4x+4)(x+2)
=(x^3+2x^2+4x^2+8x+4x+8)
=(x^3+6x^2+12x+8)

Phew, we’re done. But what if we wanted to expand a binomial that has an exponent of 4 or 5? Multiplying all of those terms together can really make your head start spinning.

Luckily, there’s an easier way. We can use Pascal’s Triangle to expand binomials. Check out my video for four examples of using Pascal’s triangle to expand binomials.

-Katie, the online math tutor