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Multiplying Complex Numbers - Concept

Teacher/Instructor 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!

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.

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