Expert: Sherry Wallin - 8/19/2010

Question
Can You please help me
A complex signal encoder sends signals through the radio waves in the form of complex equation
(x - j3y)+(y - j3x)= 2+j3
Solve the above complex equation to decode the signa

Answer
Joe, I will try to answer your question. I don't know much about radio waves but I do know how to solve complex equations. You add the real parts and they have to be equal to the real parts and you do the same with the imaginary parts so:

x -j3y + y - j3x =  x + y -j3(x+y)   all I have done is pair up the real and imaginary parts

x + y -3j(x+y) = 2 + j3

this means that x + y = 2 (real parts equal real parts) and x + y = 1 (imaginary parts equal imaginary parts) and because -j3(x+y) = -j3 that can only happen when x + y = 1

so now you have a system of equations:
x + y = 2
x + y = 1

and there is no solution to this system, just subtract the 2nd from the first and you will get 0 = 1 and that is never true.

Math Prof