3x-(1-i)(x-yi) =2+3i
Ответ
5
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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.