What is the answer to x+yi-xi+y=3 ?

The answer to x+yi-xi+y=3 is x= 3/2 ,y= 3/2

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x+yi-xi+y=3

x + y i - x i + y = 3

x = \frac{3}{2}, y = \frac{3}{2}

Solution steps

x + y i - x i + y = 3

Rewrite

x + y i - x i + y

in standard complex form:

(x + y) + (y - x) i

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

Rewrite

3

in standard complex form:

3 + 0 i

(x + y) + (y - x) i = 3 + 0 i

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

[x + y = 3 y - x = 0]

[x + y = 3 y - x = 0] : x = \frac{3}{2}, y = \frac{3}{2}

x = \frac{3}{2}, y = \frac{3}{2}

y + 1 = \frac{4}{3} (x - 3) ina

x + y i = 8 - 5

2 x - 3 x i - 5 y i + 4 = - 5 i + 4

4 x + i (3 x - y) = 3 - i^{6}

- x^{2} + 6 i x + 8 = 0