SOLUTION: True or False.... 1 + 3/(2 − i) = 5 - i Can you provide a detailed explanation of how you found the solution?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: True or False.... 1 + 3/(2 − i) = 5 - i Can you provide a detailed explanation of how you found the solution?      Log On


   

Question 188637: True or False....
1 + 3/(2 − i) = 5 - i

Can you provide a detailed explanation of how you found the solution?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1+%2B+3%2F%282+-+i%29 Start with the left side of the given equation.


1+%2B+%283%282+%2B+i%29%29%2F%28%282+-+i%29%282+%2B+i%29%29 Multiply the fraction by %282%2Bi%29%2F%282%2Bi%29 (this is to make the denominator a real number)


1+%2B+%283%282+%2B+i%29%29%2F%284-i%5E2%29 FOIL


1+%2B+%283%282+%2B+i%29%29%2F%284-%28-1%29%29 Plug in i%5E2=-1


1+%2B+%283%282+%2B+i%29%29%2F%284%2B1%29 Rewrite the denominator


1+%2B+%283%282+%2B+i%29%29%2F%285%29 Add



1+%2B+%286%2B3i%29%2F%285%29 Distribute


5%2F5+%2B+%286%2B3i%29%2F%285%29 Multiply the first term 1 by 5%2F5


%285%2B6%2B3i%29%2F%285%29 Combine the fractions


%2811%2B3i%29%2F%285%29 Combine like terms.


11%2F5%2B%283i%29%2F%285%29 Break up the fraction


Since 11%2F5%3C%3E5 and %283i%29%2F%285%29%3C%3E-i, this means that 11%2F5%2B%283i%29%2F%285%29%3C%3E5-i


So consequently 1+%2B+3%2F%282+-+i%29%3C%3E5-i

So the statement is false.