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!

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Introduction to Imaginary Numbers - 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!

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Complex numbers are a combination of real numbers and imaginary numbers, and are typically written in the form a plus bi. Where a is our real component and bi is our imaginary component. So more specifically if I’m looking at say 5 plus 8i, 8i is an imaginary numbers. So you have the square root of negative 1 we don’t know exactly what that is whereas the 5 part we do just number 5.

So whenever we are joining these two numbers, real and imaginary we refer to as a complex number. Important thing to note is that if we deal with a plus bi and b is actually 0, this imaginary piece goes away and just leaves us with a real number which is what we’ve been dealing with all along.

If a is 0, we're strictly imaginary no real component, so in essence a plus bi our complex number covers every number we ever talked about, but it also throws in this imaginary part as well. So real component imaginary component formed together, give a complex number.