Find all real numbers x and y
-2x-4-2yi=3x-2i
5x+2yi=-4+2i
5x=-4 so x=-4/5
2yi=2i so you =1
This was what I got by an online calculator said
x=-4/5-2iy/5+2i/5
y=5ix/2+2i+1
Which is right?
go to wolfram alpha and plug it in
You correctly found x and y as real numbers
The calculator solved for x in terms of y and y in terms of x.
To find the values of x and y that satisfy the given equations, let's go through the steps using proper calculations:
1. Start with the equation -2x - 4 - 2yi = 3x - 2i:
Group the real terms together and the imaginary terms together:
-2x - 4 = 3x, and -2yi = -2i
Simplify the real equation: -2x - 4 = 3x
Add 2x to both sides: -4 = 5x
Divide both sides by 5: x = -4/5
Simplify the imaginary equation: -2yi = -2i
Divide both sides by -2i: y = 1
Therefore, the values are:
x = -4/5
y = 1
2. Now, let's proceed with the second equation: 5x + 2yi = -4 + 2i
Substitute the value of x we found in the previous step:
5(-4/5) + 2yi = -4 + 2i
-4 + 2yi = -4 + 2i
Since both sides are equal, we can conclude that the imaginary part (2yi) is equal to the imaginary part (2i):
2yi = 2i
Divide both sides by 2:
yi = i
Therefore, the value of y is:
y = 1
In summary, the correct values are:
x = -4/5
y = 1
The expressions you mentioned in your question are not correct.