What is the answer to xy-xi+2iy-2i^2=-4-7i ?

The answer to xy-xi+2iy-2i^2=-4-7i is

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xy-xi+2iy-2i^2=-4-7i

x y - x i + 2 i y - 2 i^{2} = - 4 - 7 i

(x = 4, y = - \frac{3}{2} x = 3, y = - 2)

Solution steps

x y - x i + 2 i y - 2 i^{2} = - 4 - 7 i

Simplify

x y - x i + 2 i y - 2 i^{2} : (x y + 2) + i (- x + 2 y)

(x y + 2) + i (- x + 2 y) = - 4 - 7 i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[x y + 2 = - 4 - x + 2 y = - 7]

[x y + 2 = - 4 - x + 2 y = - 7] : (x = 4, y = - \frac{3}{2} x = 3, y = - 2)

(x = 4, y = - \frac{3}{2} x = 3, y = - 2)

15 - 3 y i = 12 x + 2 i

(x + y i)^{2} = - 9 - 40 i

\frac{x ^{2}}{2 i} - 2 = 0

(x - y i)^{2} = - 8 - 6

x^{2} - 7 x + 9 y i = y^{2} i + 20 y i - 12

What is the answer to xy-xi+2iy-2i^2=-4-7i ?
The answer to xy-xi+2iy-2i^2=-4-7i is