SOLUTION: what is the standard form of the expression 2-5i/4+2i? and i need to know how to work it out

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: what is the standard form of the expression 2-5i/4+2i? and i need to know how to work it out      Log On


   

Question 303828: what is the standard form of the expression 2-5i/4+2i? and i need to know how to work it out
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282-5i%29%2F%284%2B2i%29 Start with the given expression.


%28%282-5i%29%2F%284%2B2i%29%29%28%284-2i%29%2F%284-2i%29%29 Multiply the fraction by %284-2i%29%2F%284-2i%29.


%28%282-5i%29%284-2i%29%29%2F%28%284%2B2i%29%284-2i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%288-4i-20i%2B10i%5E2%29%2F%2816-8i%2B8i-4i%5E2%29 Multiply.


%288-4i-20i%2B10%28-1%29%29%2F%2816-8i%2B8i-4%28-1%29%29 Replace i%5E2 with -1.


%288-4i-20i-10%29%2F%2816-8i%2B8i%2B4%29 Multiply


%28-2-24i%29%2F%2820%29 Combine like terms.


%28-2%29%2F%2820%29%2B%28%28-24%29%2F%2820%29%29i Break up the fraction.


-1%2F10-%286%2F5%29i Reduce.


So %282-5i%29%2F%284%2B2i%29=-1%2F10-%286%2F5%29i.


So the expression is now in standard form a%2Bbi where a=-1%2F10 and b=-6%2F5