About Us

Students have an amazing amount of value to offer one another, but most of that goes unrealized.

Our mission is to personalize higher education by allowing students to teach one another, in every format possible. Read our story in the main site menu.


    Imaginary Numbers and Euler’s Formulas Review

    Updated: Jan 10

    A lot of people seem to freak out when they see an i in math or j in electrical engineering. So hopefully this will help.

    The first thing we want to go over is what i and j even are.

    The other aspect of imaginary numbers that will help us understand how they are used in electrical engineering (and systems/signaling in general) is that they can be graphed on a complex plane.

    NOTE: You may have also noticed that when we were graphing z = (x,y) on the complex plane we formed a right triangle. So:


    Looking at imaginary numbers like this, we can also see how they can be added, subtracted, and multiplied like any other numbers.

    There are also a couple of new operations:

    You may have noticed that I did not include division, and multiplication is a little difficult as well. For this, we will use Euler’s formulas.

    The four underlined formulas are the common forms of Euler’s formula

    Multiplying and dividing exponentials is a lot easier than multiplying and dividing complex numbers

    If we were asked to change that back into a complex number, then:

    These are a few more useful forms of euler’s formulas:

    These techniques are most useful in electrical engineering when dealing with AC circuits, or in other words, circuits with sinusoidal inputs

    Book a Tutoring Session

    Shayan Raofi

    March 28, 2020

    View Profile

    Book a Tutoring Session