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!
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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) (Show Source): You can put this solution on YOUR website!
First perform ^2)
using FOIL: 4\ =\ 5\ -\ 12i)
remembering that 
Then do (3\ +\ 2i)\ =\ 15\ +\ 10i\ -\ 36i\ -\ (-1)24\ =\ 39\ -\ 26i)
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 (a\ -\ bi)\ =\ a^2\ -\ (-1)b^2\ =\ a^2\ +\ b^2)
\left(\frac{5\ +\ i}{5\ +\ i}\right))
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
My calculator said it, I believe it, that settles it
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