What is the answer to (2x)/(1+x-yi)=3-4i ?

The answer to (2x)/(1+x-yi)=3-4i is x=-25/19 ,y= 8/19

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(2x)/(1+x-yi)=3-4i

\frac{2 x}{1 + x - y i} = 3 - 4 i

x = - \frac{25}{19}, y = \frac{8}{19}

Solution steps

\frac{2 x}{1 + x - y i} = 3 - 4 i

Multiply both sides by

1 + x - i y

\frac{2 x}{1 + x - y i} (1 + x - i y) = 3 (1 + x - i y) - 4 i (1 + x - i y)

Expand

2 x = (3 + 3 x - 4 y) + i (- 4 - 3 y - 4 x)

Rewrite

2 x

in standard complex form:

2 x + 0 i

2 x + 0 i = (3 + 3 x - 4 y) + i (- 4 - 3 y - 4 x)

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

[2 x = 3 + 3 x - 4 y 0 = - 4 - 3 y - 4 x]

[2 x = 3 + 3 x - 4 y 0 = - 4 - 3 y - 4 x] : x = - \frac{25}{19}, y = \frac{8}{19}

x = - \frac{25}{19}, y = \frac{8}{19}

12 i + 12 y i^{2} = - 24 x i + 6

a - bi = (a + bi) i

3 x + (y - 2) i = (5 - 2 x) + (3 y - 8) i

+ 28 + 2 i + z^{2} = 30 - 2 i, z^{1} = 3

(5 x - 2 y) + (8 x + 10 y) i = 38 + 8 i

What is the answer to (2x)/(1+x-yi)=3-4i ?
The answer to (2x)/(1+x-yi)=3-4i is x=-25/19 ,y= 8/19