find all real numbers x and y that satisfy
-2x-1-2yi=4x-5i
I think the first step is rewrite with constant complex on one side.
-2x-2yi-4x=1-5i
now I'm lost
To solve the equation -2x - 1 - 2yi = 4x - 5i, you're correct in rewriting it with the constant complex on one side. However, there was a small error in your calculation. It should be:
-2x - 2yi - 4x = 1 - 5i
Next, combine like terms:
-6x - 2yi = 1 - 5i
To get the real part and the imaginary part on separate sides, separate the equation into two parts:
-6x = 1 (1)
-2yi = -5i (2)
Now, let's solve equation (1) for x:
-6x = 1
Divide both sides by -6:
x = 1/(-6)
Simplifying further:
x = -1/6
Now, let's solve equation (2) for y:
-2yi = -5i
Divide both sides by -2i:
y = (-5i) / (-2i)
-i and -i can be canceled out, resulting in:
y = 5/2
So, the solution to the given equation is:
x = -1/6
y = 5/2
Hence, the real numbers x and y that satisfy the equation -2x - 1 - 2yi = 4x - 5i are x = -1/6 and y = 5/2.