To solve the equation 2 + 3i + x + yi = 6, we will start by isolating the variables. First, we rewrite the equation:
Rearranging gives us:
x + yi = 6 – (2 + 3i)
This simplifies to:
x + yi = 4 – 3i
Now we can separate the real part and the imaginary part. In the expression x + yi, x represents the real component, and yi represents the imaginary component. Thus, we have:
- Real part: x = 4
- Imaginary part: y = -3
Now that we have the values of x and y, we can calculate xy:
x * yi = 4 * (-3i) = -12i
Therefore, the value of x multiplied by yi is:
-12i
In conclusion, if 2 + 3i + x + yi = 6, then the value of x * yi is -12i.