- #1
159753x
- 17
- 0
I have a few complex equations that I am having trouble solving for homework.
Solve for all possible values of the real numbers x and y.
A. (x+iy)2 = (x-iy)2
B. (x + iy + 2 + 3i)/(2x + 2iy - 3) = i + 2
C. Abs[1 - (x + iy)] = x + iy
The example problem in the book says that we should separately solve the real and complex parts. That is what I try to do.
A. Expanding both sides, I simply get x2 - y2 = x2 - y2 for the real parts. I don't know what to do with that information.
For the imaginary parts, I get 2ixy = -2ixy. So I get plus-or-minus y = plus-or-minus x.
The answer in the back is x = 0 for any real y OR y = 0 for any real x. How did they get this?
B. Again, separating out the real and imaginary components:
(x + 2)/(2x - 3) = 2
Solving this, I get 8/3.
For the imaginary part, I get (y + 3)/(2y) = 1. This yields y = 3.
The answer in the back is x = 36/13 and y = 2/13.
C. I don't know how to deal with the absolute value in this one. The answer is y = 0, x = 1/2.I solved many other problems using the separation of real and imaginary components strategy, but these don't seem to work. Some help would be appreciated!
Homework Statement
Solve for all possible values of the real numbers x and y.
A. (x+iy)2 = (x-iy)2
B. (x + iy + 2 + 3i)/(2x + 2iy - 3) = i + 2
C. Abs[1 - (x + iy)] = x + iy
Homework Equations
The example problem in the book says that we should separately solve the real and complex parts. That is what I try to do.
The Attempt at a Solution
A. Expanding both sides, I simply get x2 - y2 = x2 - y2 for the real parts. I don't know what to do with that information.
For the imaginary parts, I get 2ixy = -2ixy. So I get plus-or-minus y = plus-or-minus x.
The answer in the back is x = 0 for any real y OR y = 0 for any real x. How did they get this?
B. Again, separating out the real and imaginary components:
(x + 2)/(2x - 3) = 2
Solving this, I get 8/3.
For the imaginary part, I get (y + 3)/(2y) = 1. This yields y = 3.
The answer in the back is x = 36/13 and y = 2/13.
C. I don't know how to deal with the absolute value in this one. The answer is y = 0, x = 1/2.I solved many other problems using the separation of real and imaginary components strategy, but these don't seem to work. Some help would be appreciated!