Question

3x-(1-i)(x-yi) =2+3i​

Answer 1

Let's start by expanding the expression on the left-hand side using distributive property:

3x - (1 - i)(x - yi) = 2 + 3i

3x - (x - yi) + i(x - yi) = 2 + 3i

3x - x + yi + ix - iy = 2 + 3i

(3 - 1) x + (1 - 1) yi + ix = 2 + 3i

2x + i(x - y) = 2 + 3i

Now we have a complex equation in the form a+bi=c+di. To solve for x and y, we need to separate the real and imaginary parts of the equation:

Real part: 2x = 2 (dividing both sides by 2)

x = 1

Imaginary part: x - y = 3/2

y = x - 3/2 = 1 - 3/2 = -1/2

Therefore, the solution is x = 1, y = -1/2.