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

The answer to (x+iy)+2(x-iy)=(2i)/(1+3i) is x= 1/5 ,y=-1/5

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(x+iy)+2(x-iy)=(2i)/(1+3i)

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

x = \frac{1}{5}, y = - \frac{1}{5}

Solution steps

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

Expand

3 x - i y = \frac{3}{5} + \frac{i}{5}

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

[3 x = \frac{3}{5} - y = \frac{1}{5}]

[3 x = \frac{3}{5} - y = \frac{1}{5}] : x = \frac{1}{5}, y = - \frac{1}{5}

x = \frac{1}{5}, y = - \frac{1}{5}

3 i y^{2} - y + 2 i = 0

x (1 + i)^{2} + y (2 - i)^{2} = 3 + 10 i

z^{2} - (5 + 2 i) z + 2 = 0

x + i y - 1 + i = 3

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

What is the answer to (x+iy)+2(x-iy)=(2i)/(1+3i) ?
The answer to (x+iy)+2(x-iy)=(2i)/(1+3i) is x= 1/5 ,y=-1/5