## Imaginary Numbers: Simplifying 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??”) However, fear not, they’re really not bad! Today we’ll be looking at 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 by using the fact that i^2 = -1. First we’ll go over a few small exponents to get the hang of it, and then we’ll do four problems with large exponents.

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 ðŸ™‚

-Katie, the online math tutor (and North Portland math tutor!)

# How to Tutor Online: Get started quickly!

Are you thinking about online tutoring? Maybe you’re a teacher looking for additional income, a stay-at-home parent wanting a flexible way to make money, or a college student. I know what you’re asking: How do I tutor online? To learn how to tutor online, read on!

## Option 1: How to Tutor Online for an Organization as an Independent Contractor

There are many organizations that pay \$11-16 / hour to tutor as an independent contractor. Some companies will have you work a set schedule like QkidsÂ (teach English to children in China via video, audio, and Qkids software) and Yup (tutor math, physics, or chemistry via text).

Other companies allow the most flexibility by allowing you to work whenever you want, like Chegg (tutor any subject via text and whiteboard). The caveat with Chegg is that you only get paid for when you’re actually working with a student, and it can take a while to actually be working with a student.

There are a lot more companies out there just like the ones I listed above. Any of these companies can get you tutoring online within a couple weeks, sometimes sooner. If those sound appealing, check them out!

I’ve actually worked for most of the companies listed above, so if you have any questions or want any advice, comment below with your questions. I’m happy to share my experiences.

## Option 2: How to Tutor Online Independently

Maybe you want to bypass these organizations though and tutor for yourself like I do at Katie Tutors Math. This will require you to do extra work like marketing, figuring out the logistics of tutoring online, handling customer service for your clients, and payment processing. However, unlike working for an organization, you’ll also be able to choose your own rate and have complete control over how many hours you work, your schedule, and which clients you take on. Freedom, baby!

Maybe you’re interested in tutoring online independently, but it seems intimidating? Not to fear! I’m here to make this process a lot easier for you and start answering your questions. We’ll start with the most critical question:

### How do I tutor online?

To tutor online, you’ll need two things:

• a way to talk to the student
• a way to visually show (and perhaps share) material with students

First, let’s start with how to talk to your student online. My favorite tool to use is Skype because it’s simple and nearly everyone has heard of it if not used it themselves. With Skype you can use only the audio to hear each other, or you can turn on video too in order to see each other. Not a fan of Skype? Try Facetime or Google Hangouts. Most importantly, I recommend investing a few dollars in a headset so that the student can clearly hear you without the excess background noise of your dog or air conditioner. It’ll speak highly to your professionalism!

#### Online Whiteboard

The second part of how to tutor online is presenting material to students or sharing a workspace. The best solution for this is typically an online whiteboard. With an online whiteboard, simply share the link with your student, and you instantly have a workspace for just the two of you. If you’ve never used an online whiteboard before, you’re in for a treat! Bitpaper and ScribblarÂ have the best online whiteboards on the market right now for online tutors.

Here are some online whiteboard features to look forward to:

• You can each write and see what the other person is writing in real time
• Use different colors, thickness, and shapes to bring your teaching to life
• Easily upload pdf’s or images of homework or a textbook and work on the problems together
• Use multiple pages of a whiteboard to keep your work organized
• At the end save all of it to a pdf to share with your student

#### Tablet

You can use your computer mouse to write on a whiteboard, but it can be difficult to write legibly. Not to mention that using your mouse to write out equations or verb charts gets old quickly! Instead, I recommend investing in aÂ tablet. With a tablet you can write on your online whiteboard naturally, just as you do on paper. And if your student will be writing on the whiteboard often, have them get a tablet as well! I use a wacom bamboo tablet (pictured above) and love it.

#### Practice

Once you’ve chosen your software and have your materials, try a practice session. Tell a friend that you’re learning how to tutor online and you need a practice student. You’ll be able to work out all the kinks and make sure you’re confidently able to introduce a student to the technology and have a successful session.

Send an email to your friend just like you would to a new student. Include a link to the whiteboard as well as information about how to connect to audio/video chat (whether that’s Skype or something else).

During the session, try using the whiteboard, uploading PDF’s, sharing your screen, anything you might do while tutoring!

Then you’re ready to get started with a student!

#### A note about Zoom

While I don’t use Zoom myself, I want to mention it here as many online tutors love it. Zoom is a video conferencing software that combines audio and video capabilities as well as a built-in whiteboard. The whiteboard is not as robust as an independent whiteboard (most notably, it has only one page). However some tutors need to only present information or have no need for the student to be able to write or point at things on the whiteboard. In this case, try using Skype or Zoom and then share your presentation with the student (through the “share your screen or window” feature). For a presentation software, use Powerpoint, OneNote, Prenzi, or anything you’re comfortable with!

### In conclusion, how to tutor online–the tools you need:

Finally, don’t forget to ask a friend to practice with you!

To be notified when I post the next article in the series “How to Tutor Online” sign up here. If you’re itching to learn more right now about how to get started, check out theÂ The Top 5 Tools for Online Math TutorsÂ to learn about the best payment service, scheduling system, and support group!

# 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 andÂ Division — do these from left to right.
4. Addition andÂ 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