All real # x and y that satisfy
-2x-1+2yi=4x-5i
first step is place constant complex # on one side
-2x+2yi-4x=1+5i
-6x+2yi=1+5i
now I'm lost
for two complex numbers to be equal, the real and imaginary parts must be equal. So, we need
-2x-1 = 4x
2y = -5
That should help, eh?
So how did you decided the 1 went with the x's and not the other equation.
After placing the constant complex number on one side, which you correctly did, the equation becomes:
-2x + 2yi - 4x = 1 + 5i
Now, let's simplify further:
-6x + 2yi = 1 + 5i
To solve for x and y in this equation, you need to isolate each variable.
First, let's isolate y by moving the term with y to the left side of the equation:
2yi = -6x + 1 + 5i
Next, divide both sides by 2i to solve for y:
y = (-6x + 1 + 5i) / (2i)
Now, let's isolate x by moving the term with x to the left side of the equation:
-6x = 1 + 5i - 2yi
Next, divide both sides by -6 to solve for x:
x = (1 + 5i - 2yi) / -6
Therefore, the solution to the equation is:
x = (1 + 5i - 2yi) / -6
y = (-6x + 1 + 5i) / (2i)
By substituting different values for x, you can find corresponding values for y that satisfy the equation.