SOLUTION: How do you solve (3-2i)^2(3+2i)/(5-i)? The answer from the book is: 17/2 - 7/2 i I don't know how they got this answer. Please help!

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: How do you solve (3-2i)^2(3+2i)/(5-i)? The answer from the book is: 17/2 - 7/2 i I don't know how they got this answer. Please help!       Log On


   

Question 517383: How do you solve (3-2i)^2(3+2i)/(5-i)? The answer from the book is:
17/2 - 7/2 i
I don't know how they got this answer. Please help!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


First perform using FOIL: remembering that

Then do

Now you have:

To rationalize the denominator, multiply the whole fraction by 1 in the form of the conjugate of the denominator divided by itself. Remember that if you have a number , then its conjugate is and that the product of two conjugates is the difference of two squares, so



With careful arithmetic you will get an integer denominator that can be divided into each of the resulting coefficients in the numerator. Remember that 8.5 is the same as 17/2.

John

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