SOLUTION: assignment is to simplify this expression: (3-i)^-2 i get as far as 1/(9-6i+i^2) answers sheet says correct answer is (4+3i)/50 can you help me figure out how to get that

Question 78176: assignment is to simplify this expression: (3-i)^-2
i get as far as 1/(9-6i+i^2)
answers sheet says correct answer is (4+3i)/50
can you help me figure out how to get that answer?

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression
Invert
Foil
replace with (-1) Since
Combine like terms
Multiply the numerator and denominator by the complex conjugate this will rationalize the denominator (ie it will get rid of the i term in the denominator)
Multiply
Foil
Combine like terms
Replace with (-1)
Multiply -36 by -1
Combine like terms
Factor out a 2
Divide
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
simplify this expression: (3-i)^-2 = 1/(3-i)^2
Multiply numerator and denominator by (3+i)^2 to get:
---------
(3+i)^2 / 10^2
= (9+6i-1)/100
= (8+6i)/100
= (4+3i)50
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