SOLUTION: (2w+i)/(w-i) = (3w+4i)/(w+3i) I have tried solving this by bringing one side over to the other, making a common denominator, and subtracting, and setting it equal to zero, but t

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: (2w+i)/(w-i) = (3w+4i)/(w+3i) I have tried solving this by bringing one side over to the other, making a common denominator, and subtracting, and setting it equal to zero, but t      Log On


   

Question 375712: (2w+i)/(w-i) = (3w+4i)/(w+3i)
I have tried solving this by bringing one side over to the other, making a common denominator, and subtracting, and setting it equal to zero, but then I get stuck. There must be some trick to this. I appreciate you looking at this problem. =)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
%282w%2Bi%29%2F%28w-i%29+=+%283w%2B4i%29%2F%28w%2B3i%29. Cross-multiply to get
%282w%2Bi%29%28w%2B3i%29=+%283w%2B4i%29%28w-i%29+,
2w%5E2+%2B+6iw+%2B+iw+%2B+3i%5E2+=+3w%5E2+-+3iw+%2B+4iw+-+4i%5E2, or
2w%5E2+%2B7iw+-+3+=+3w%5E2+%2B+iw+%2B+4, or
0+=+w%5E2+-+6iw+%2B+7,
0 = (w -7i )(w + i), giving
w = 7i or w = -i. Since none of these values make the denominators of the original equation equal to zero, these are the final answers.