SOLUTION: How do you solve division problems of complex numbers: -5 + 3i / -6 - 6i My final exam is tomorrow and I am so confused on how to divide these and also on how to multiply:

Question 617745: How do you solve division problems of complex numbers:
-5 + 3i / -6 - 6i
My final exam is tomorrow and I am so confused on how to divide these and also on how to multiply:
7(2-6i)(1-7i)
Do you use the FOIL method or do you distribute?
Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Your second question: "Do you use the FOIL method or do you distribute?" Um...FOIL and distribute are the same thing. FOIL is just repeating the distribution a couple of times. So the answer is yes.

When you have FOILed the two binomials, distribute the 7.

First question:

Multiply your complex fraction by 1 in the form of the conjugate of the denominator divided by itself. The conjugate of is .

So, multiply your fraction by . It might help to remember that the product of a pair of conjugates is the difference of two squares, but also remember .

John

My calculator said it, I believe it, that settles it

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
(-5 + 3i) / (-6 - 6i)
you have to remove the imaginary number from the denominator by multiplying it by it's conjugate.
the conjugate of (-6 - 6i) is equal to (-6 + 6i)
you multiply those together using the distributive law of multiplication.
you get:
(-6 - 6i) * (-6 + 6i) equals:
(-6) * (-6 + 6i) - (6i) * (-6 + 6i)
this becomes:
(-6) * (-6) + (-6) * (6i) - (6i) * (-6) + (-6i) * (6i)
you perform the indicated multiplications to get:
+ 36 - 36i + 36i - 36 * i^2
the -36i and the + 36i cancel out and you are left with:
36 - 36 * i^2
since i^2 is equal to -1, then you are left with:
36 - 36 * (-1) equals:
36 + 36 which is equal to:
72
your denominator becomes 72.
if you multiply your denominator by (-6 + 6i), then you also have to multiply the numerator by (-6 + 6i) in order to keep the fraction equivalent.
you are now left with:
(-5 + 3i) * (-6 + 6i) / 72
you do the distributive multiplication thing again in the numerator to get:
30 - 30i - 18i + 18i^2
you combine like terms to get:
30 - 48i + 18i^2
since i^2 = (-1), you get:
30 - 48i - 18 which then becomes:
12 - 48i
that's in the numerator.
the denominator is 72
your expression becomes:
12 - 48i / 72 which then becomes:
12 / 72 - 48i / 72 because you need to keep the real part and the imaginary part separate.
your final answer is:
12/72 - 48i/72
since 12/72 is equivalent to 1/6 and 48/72 is equivalent to 2/3, then your answer becomes:
1/6 - (2/3)i
looks like you need a refresher course on how to do complex number arithmetic.
try these websites:
http://www.purplemath.com/modules/complex.htm
http://www.mathsisfun.com/numbers/complex-numbers.html
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut12_complexnum.htm
browse each website.
pick the one that makes the most sense to you and is the easiest to understand.
-----
foil and distributive property are the same thing.
foil is just a subset of the distributive process.
yes - you would use foil.
yes - you would use the distributive property of multiplication.
write if you have further questions.
check out the references.
they will help explain it as well.

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