SOLUTION: HI! May I get some help with this expression? Evaluate the expression and write the result in the form a + bi. (6 + 5i)^-1

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: HI! May I get some help with this expression? Evaluate the expression and write the result in the form a + bi. (6 + 5i)^-1      Log On


   

Question 120434: HI! May I get some help with this expression?
Evaluate the expression and write the result in the form a + bi.
(6 + 5i)^-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%286+%2B+5i%29%5E-1 Start with the given expression



1%2F%286+%2B+5i%29 Rewrite the expression as 1%2F%286+%2B+5i%29. Remember, x%5E-2=1%2Fx%5E2

Multiply the fraction by

Foil and Multiply


Break up the fraction. So it is now in a%2Bbi form where a=6%2F61 and b=-5%2F61


So simplifies to


In other words,