To solve the equation 5yi = x + 3i, we need to isolate the real and imaginary components of the equation.
First, let’s rewrite the original equation in a clearer format:
- Left Side: 5yi (this has a real part 0 and an imaginary part 5y)
- Right Side: x + 3i (this has a real part x and an imaginary part 3)
Next, we can equate the real parts and the imaginary parts of both sides:
- Real part: 0 = x
- Imaginary part: 5y = 3
From the real part, we directly find:
x = 0
From the imaginary part, we can solve for y:
5y = 3
=> y = 3/5 = 0.6
Thus, the solution is:
- x = 0
- y = 0.6
In summary, the values that satisfy the equation are:
x = 0 and y = 0.6.