Question

Determine X and Y for

(2+i)(x+yi)=−7+3i.

Answer 1

To determine the values of X and Y in the equation (2+i)(x+yi) = -7+3i, we can use the distributive property of complex numbers. After multiplying the real parts and the imaginary parts separately, we can solve for X and Y by setting the real and imaginary parts equal to each other. The values of X and Y are X = -7/2 and Y = 13/4.

Step-by-step explanation:

To determine the values of X and Y in the equation (2+i)(x+yi) = -7+3i, we can use the distributive property of complex numbers.

1. Multiply the real parts: 2x = -7
2. Multiply the imaginary parts: xi + 2yi = 3i
3. Simplify the second equation by separating the real and imaginary parts: xi + 2yi = 0 + 3i
4. Set the real parts equal to each other: 2x = -7
5. Set the imaginary parts equal to each other: xi + 2yi = 3i
6. Substitute x = -7/2 into the second equation: (-7/2)i + 2yi = 3i
7. Simplify and solve for y: -7i/2 + 2yi = 3i
8. Multiply through by 2 to eliminate fraction: -7i + 4yi = 6i
9. Combine like terms: (4y - 7)i = 6i
10. Set the real parts equal to each other: (4y - 7) = 6
11. Solve for y: 4y = 13, y = 13/4.

Therefore, the values of X and Y are X = -7/2 and Y = 13/4.