SOLUTION: 6 _____ 5 + i i am suppose to write the result in standard form.

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 6 _____ 5 + i i am suppose to write the result in standard form.      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 219581: 6
_____
5 + i
i am suppose to write the result in standard form.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
6%2F%285%2Bi%29 Start with the given expression.


%286%2F%285%2Bi%29%29%28%285-i%29%2F%285-i%29%29 Multiply the fraction by %285-i%29%2F%285-i%29.


%286%285-i%29%29%2F%28%285%2Bi%29%285-i%29%29 Combine the fractions.


%28%286%29%285%29%2B%286%29%28-i%29%29%2F%28%285%2Bi%29%285-i%29%29 Distribute


%28%286%29%285%29%2B%286%29%28-i%29%29%2F%28%285%29%285%29%2B%285%29%28-i%29%2B%28i%29%285%29%2B%28i%29%28-i%29%29 FOIL the denominator.


%2830-6i%29%2F%2825-5i%2B5i-i%5E2%29 Multiply.


%2830-6i%29%2F%2825-5i%2B5i-%28-1%29%29 Replace i%5E2 with -1.


%2830-6i%29%2F%2825-5i%2B5i%2B1%29 Simplify


%2830-6i%29%2F%2826%29 Combine like terms.


%2830%29%2F%2826%29%2B%28%28-6%29%2F%2826%29%29i Break up the fraction.


15%2F13-%283%2F13%29i Reduce.


So 6%2F%285%2Bi%29=15%2F13-%283%2F13%29i which is in standard form a%2Bbi where a=15%2F13 and b=-3%2F13