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Adding and Subtracting Complex Numbers - Concept 16,323 views

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!

Subtracting and adding complex numbers is the same idea as combining like terms. In an expression, the coefficients of i can be summed together just like the coefficients of variables. If an expression has real numbers and square roots of negative numbers, rewrite using i and then combine like terms.

Adding and subtracting complex numbers. So if you think back to how we work with any normal number, we just add and when you add and subtract. We just combine like terms. So with this example up here 8x-4+3x+2. If I said simplify this out you would just combine like terms. So we have our 8x and our 3x, this become 11x. -4+2 just becomes -2. You combine like terms. When you're dealing with complex and imaginary numbers, it's really no different. Okay? So here I have a problem 4i-3+2. I can just combine my imaginary numbers and my non-imaginary numbers.
So, 4i-3+2i, 4i and 2i can be combined to be 6i. -3 doesn't have anything to join with so we end up with just -3. Really no different than anything else, just combining your like terms.

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