What is the answer to x^2+2y^2+xi+yi=xy+7+3i ?

The answer to x^2+2y^2+xi+yi=xy+7+3i is

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x^2+2y^2+xi+yi=xy+7+3i

x^{2} + 2 y^{2} + x i + y i = x y + 7 + 3 i

(x = 1, x = \frac{11}{4}, y = 2 y = \frac{1}{4})

Solution steps

x^{2} + 2 y^{2} + x i + y i = x y + 7 + 3 i

Rewrite

x^{2} + 2 y^{2} + x i + y i

in standard complex form:

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

(x^{2} + 2 y^{2}) + (x + y) i = x y + 7 + 3 i

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

[x^{2} + 2 y^{2} = x y + 7 x + y = 3]

[x^{2} + 2 y^{2} = x y + 7 x + y = 3] : (x = 1, x = \frac{11}{4}, y = 2 y = \frac{1}{4})

(x = 1, x = \frac{11}{4}, y = 2 y = \frac{1}{4})

∣ z ∣ + z - z \cdot z = 3 + 3 i

6 x + 12 y i = (2 x - 3) + (2 y + 3) i

15 + 2 3 x = - 5 x + 2

x^{2} = - 3 i

3 x + 2 x i - 3 y i + 2 y = 0

What is the answer to x^2+2y^2+xi+yi=xy+7+3i ?
The answer to x^2+2y^2+xi+yi=xy+7+3i is