Answer:
Therefore, the solution to the equation -6 + 24i = 3x + 5xi - 3yi + 5y is:
x = -4.8 and y = -3.8.
Explanation:
To solve this equation, we need to separate the real and imaginary parts on each side of the equation. The real part of the left-hand side is -6, and the real part of the right-hand side is 3x - 3y. Therefore, we have:
-6 = 3x - 3y
Simplifying this equation, we get:
2x - 2y = -2
Dividing both sides by 2, we get:
x - y = -1
Now let's look at the imaginary parts. The imaginary part of the left-hand side is 24i, and the imaginary part of the right-hand side is 5xi + 5y. Therefore, we have:
24i = 5xi + 5y
Dividing both sides by 5, we get:
4.8i = xi + y
Since x and y are real numbers, their imaginary parts are both 0. Therefore, we have:
4.8i = xi
Dividing both sides by i, we get:
x = -4.8
Now that we know x, we can substitute it into our equation for x - y, which gives us:
-4.8 - y = -1
Adding y to both sides, we get:
-4.8 = y - 1
Adding 1 to both sides, we get:
-3.8 = y
Therefore, the solution to the equation -6 + 24i = 3x + 5xi - 3yi + 5y is:
x = -4.8 and y = -3.8.