How You Can (And Should) Get More Practice!

Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for you.

Theoretically Easier Difficulty Problem

When adding or subtracting complex numbers, you can just add (or subtract) the individual parts independently.
Simplify the following into form:

Theoretically Medium Difficulty Problem

When multiplying complex numbers, you want to distribute out the terms, like you are multiplying two binomials.
Don’t forget that , so the two imaginary parts being multiplied together give you a real number!
Simplify the following into form:

Theoretically Harder Difficulty Problem

When simplifying division of complex numbers, you need to multiply the top and bottom of the fraction by the complex conjugate of the bottom number.
To get the complex conjugate of a complex number, you just need to flip the sign in front of the imaginary number.
In this case, we want to multiply the top and bottom by , so we want to compute: .
Simplify the following into form: