Questions on Algebra: Real numbers, Irrational numbers, etc answered by real tutors!

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Question 151802: (7-i)/(-1+3i): (7-i)/(-1+3i)
Answer by Edwin McCravy(2043) About Me  (Show Source):
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(7-i)/(-1+3i)

Form the conjugate of the denominator by
1. Writing the first term.   -1
2. Beside the first term write the second
term with the sign before it changed. 
                             -1-3i

Put parentheses around top and bottom of original:

((7-i))/((-1+3i))

Multiply top and bottom by the conjugate of the
denominator placed in parentheses:

((7-i)(-1-3i))/((-1+3i)(-1-3i))  

Now use FOIL to multiply out the top and bottom:

(-7-21i+i+3i^2)/(1+3i-3i-9i^2))

Combine like terms:

(-7-20i+3i^2)/(1-9i^2))

Replace both i^2's by -1:

(-7-20i+3(-1))/(1-9(-1)))

Simplify:

(-7-20i-3)/(1+9)

Simplify further:

(-10-20i)/10

Make two fractions:

-10/10-20i/10

Simplify:

-1-2i

Edwin