 ###### 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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# Multiplying Complex Numbers - Concept

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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To simplify expressions by multiplying complex numbers, we use exponent rules for i and then simplify further if possible. Remember that, by definition, i^2= -1, which also means that i ^ 4= 1. If multiplying two square roots of negatives, their product is not a positive. First we rewrite the radicals using i and then multiply and simplify.

Multiplying complex numbers. So what we're going to talk about now is multiplying complex numbers or numbers that include the letter i square root of -1. So take a look at something we know how to do. Multiplying 4x times 7x. Here we just multiply and combine like terms. So the 4 gets multiplied by the 7 giving us 28 and we have the x times the x so that gives us x squared. Okay.
Very similar concept when we're dealing with i, okay? We have the 3 times 5. This would give us 15, the i times i giving us i squared. Now part of the definition of i is that i is equal to the square root of -1 but the other part is i squared is equal to -1. So using a simple substitution, we know that i squared is equal to -1. We can plug this in right here and this ends up giving us -15. So multiplying with i is pretty much the same exact thing as multiplying with anything else. Just you always have to remember whenever you see an i squared we can always substitute in -1.