Find all real numbers x and y
so I'm a bit confused with the y solution
-2x-4+2yi=3x-2i
2yi=5x-2i+4
I know the answer is
y = -5ix/2 - 2i - 1
so y = -1
But how do you go from
2yi = 5x - 2i + 4 to
y = -5ix/2 - 2i - 1
the real and imaginary parts must be equal, so
(-2x-4)+(2yi) = 3x - 2i
-2x-4 = 3x
2y = -2
x = -4/5
y = -1
as for your question, recall that since i^2 = -1, 1/i = -i
Dividing through by 2i yields the desired result.
Note also that since x = -4/5,
-5i(-4/5)/2 - 2i - 1
= 2i-2i-1
= -1
which is the solution for y.
2yi = 5x - 2i + 4
Divide everything by 2i to get y alone:
2yi / 21 = (5x - 2i + 4) / 2i
y = (5/2i)x - 1 + 2/i
Hm, I think there's a typo..
^No, I'm sorry don't mind my post ^^;
To find the solution for y in the equation 2yi = 5x - 2i + 4, we can start by isolating the term with the variable y.
1. Rearrange the equation: 2yi = 5x - 2i + 4
Move the constant terms to the right side: 2yi - 4 = 5x - 2i
Rearrange the terms: 5x - 2i = 2yi - 4
2. Separate the real and imaginary parts:
Separate each side of the equation into real and imaginary parts.
For the left side, the real part is 5x and the imaginary part is -2i.
For the right side, the real part is 0 (since it doesn't involve i) and the imaginary part is 2y.
Real part: 5x = 0
Imaginary part: -2i = 2y - 4
3. Solve for x:
From the real part, we can see that 5x = 0. Dividing both sides by 5, we get:
x = 0/5
Therefore, x = 0.
4. Solve for y:
From the imaginary part, we have -2i = 2y - 4. Add 4 to both sides:
-2i + 4 = 2y
Next, divide both sides by 2 to isolate y:
(2y) / 2 = (-2i + 4) / 2
Simplifying gives:
y = (-2i/2) + (4/2)
y = -i + 2
Finally, since y is in terms of i, we can write y = -i + 2 as y = -1.
Therefore, the solution for y is y = -1.