SOLUTION: Simplify the expression and write the result in standard a+bi form. Show all work. 1/3+i=

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Simplify the expression and write the result in standard a+bi form. Show all work. 1/3+i=      Log On


   

Question 189902: Simplify the expression and write the result in standard a+bi form. Show all work.
1/3+i=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%29%2F%283%2Bi%29 Start with the given expression.


%28%281%29%2F%283%2Bi%29%29%28%283-i%29%2F%283-i%29%29 Multiply the fraction by %283-i%29%2F%283-i%29.


%28%281%29%283-i%29%29%2F%28%283%2Bi%29%283-i%29%29 Combine the fractions.


%283-i%29%2F%28%283%2Bi%29%283-i%29%29 Distribute.


%283-i%29%2F%289-3i%2B3i-i%5E2%29 FOIL the denominator.


%283-i%29%2F%289-3i%2B3i-%28-1%29%29 Replace i%5E2 with -1


%283-i%29%2F%289-3i%2B3i%2B1%29 Simplify


%283-i%29%2F%2810%29 Combine like terms.


%283%29%2F%2810%29%2B%28%28-1%29%2F%2810%29%29i Break up the fraction.


3%2F10-%281%2F10%29i Reduce.


So %281%29%2F%283%2Bi%29=3%2F10-%281%2F10%29i.


So the expression is now in standard form a%2Bbi where a=3%2F10 and b=-1%2F10