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

The answer to (2(x+iy))/(3-(x-iy))=i is x=-1,y=2

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(2(x+iy))/(3-(x-iy))=i

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

x = - 1, y = 2

Solution steps

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

Multiply both sides by

3 - x + i y

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

Expand

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

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

[2 x = - y 2 y = 3 - x]

[2 x = - y 2 y = 3 - x] : x = - 1, y = 2

x = - 1, y = 2

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

z^{2} - (1 + 3 i) z + (2 i - 2) = 0

\frac{1 + ai}{4 + bi} = 1 + 4 i

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

z = \frac{6 + 8 ai}{2 - 3 i}

What is the answer to (2(x+iy))/(3-(x-iy))=i ?
The answer to (2(x+iy))/(3-(x-iy))=i is x=-1,y=2