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Introduction to Imaginary Numbers  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
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.
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Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
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