SOLUTION: would you please solve the following equation : xi/1-yi=3x+4i/3x+4y , where x & y are real . thank you in advance

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: would you please solve the following equation : xi/1-yi=3x+4i/3x+4y , where x & y are real . thank you in advance      Log On


   

Question 111394: would you please solve the following equation :
xi/1-yi=3x+4i/3x+4y , where x & y are real .
thank you in advance
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
xi%2F%281-yi%29+=+3x%2B4i%2F%283x%2B4y%29...........I guess, this is correct
xi%2F%281-yi%29+=+3x%2B4i%2F%283x%2B4y%29........first add the terms on right side ( common denominator is %283x%2B4y%29
xi%2F%281-yi%29+=+%283x%283x%2B4y%29%2B4i%29%2F%283x%2B4y%29........multiply both sides by %281-yi%29%283x%2B4y%29
.......cancel 1-yi on the left, and 3x%2B4y on the right side

%28xi%29%283x%2B4y%29=+%283x%283x%2B4y%29%2B4i%29%281-yi%29...........multiply
3x%5E2i+%2B+4xyi+=+%289x%5E2+%2B+12xy+%2B+4i%29%281-yi%29
3x%5E2i+%2B+4xyi+=+9x%5E2+%2B+12xy+%2B+4i+-9x%5E2yi+-+12xy%5E2i+-+4yi%5E2

3x%5E2i+%2B+4xyi+=+9x%5E2+%2B+12xy+%2B+4i+-+9x%5E2yi+-+12xy%5E2i+%2B+4y


+0+=+-+3x%5E2i+-+4xyi+%2B+%289x%5E2+%2B+12xy%29%281+-+yi%29+%2B+4%28y+%2B+i%29

+0+=++%2B+3x%5E2%283+-+i%29++%2B+4xy%283+-+i%29+-3xy%283xi+-+4yi%29+%2B+4%28i+%2B+y%29

+0+=++%283x%5E2+%2B+4xy%29%283+-+i%29+-3xy%283xi+-+4yi%29+%2B+4%28i+%2B+y%29