SOLUTION: what is an equivalent form of 2/3+ i? my four options are 3-i/4, 3-i/5, 4-i/4 and 4-i/5. please help i have no idea how to do this problem!!!

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: what is an equivalent form of 2/3+ i? my four options are 3-i/4, 3-i/5, 4-i/4 and 4-i/5. please help i have no idea how to do this problem!!!       Log On


   

Question 80485: what is an equivalent form of 2/3+ i? my four options are 3-i/4, 3-i/5, 4-i/4 and 4-i/5. please help i have no idea how to do this problem!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%283%2B+i%29

%282%2F%283%2B+i%29%29%28%283-i%29%2F%283-i%29%29 Multiply both top and bottom by the complex conjugate 3-i

%282%283-i%29%29%2F%283%2B+i%29%283-i%29%29 Multiply

%286-2i%29%2F%289-i%5E2%29 Distribute and foil

Since i%5E2=-1 we can say

%286-2i%29%2F%289-%28-1%29%29

%286-2i%29%2F%289%2B1%29

%286-2i%29%2F%2810%29

Now factor out 2 out of the top and bottom

2%283-i%29%2F2%285%29

%283-i%29%2F%285%29 Simplify

So 2%2F%283%2B+i%29 is equivalent to %283-i%29%2F%285%29