Question 488110: (-4+6i)(-3+7i)
Found 2 solutions by Jstrasner, richard1234:
Answer by Jstrasner(112)   (Show Source):
You can put this solution on YOUR website! Hey,
So for this problem we need to do what is called Foiling, which is a special way of solving these types of problems, which are called polynomials.
So first we multiply the first variable in each parentheses:
(-4+6i)(-3+7i) => -4 x -3 = 12
Then the first variable in the first parentheses is multiplied by the second variable in the second parentheses:
(-4+6i)(-3+7i) => -4 x 7i = -28i
Then the second variable in the first parentheses is multiplied by the first variable in the second parentheses:
(-4+6i)(-3+7i) => 6i x -3 = -18i
Finally the second variable in the first parentheses is multiplied by the second variable in the second parentheses:
(-4+6i)(-3+7i) => 6i x 7i = 42(i^2). Now when i is squared it becomes -1, so the result is actually -42.
Now we add all of the results that we got from foiling:
12 + (-28i) + (-18i) + (-42) = -30 - 46i
So the answer is -30 - 46i
I hope this helps!
Answer by richard1234(7193)  (Show Source):
You can put this solution on YOUR website! The other tutor is referring to it as FOIL (instead of foil) because FOIL is an acronym for "first, outer, inner, last," an order in which you can multiply two binomials. For example,
(-4+6i)(-3+7i) = (-4)(-3) + (-4)(7i) + (6i)(-3) + (6i)(7i)
= 12 - 28i - 18i - 42
= -30 - 46i
The textbook writers must have come up with FOIL pretty recently. I don't remember learning that acronym in my algebra class...and I'm a senior in HS so it's only been 5 or so years since I learned algebra.
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