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

The answer to (x+iy)+2(x-iy)=(2i)/(1+2i) is x= 4/15 ,y=-2/5

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

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

x = \frac{4}{15}, y = - \frac{2}{5}

Solution steps

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

Expand

3 x - i y = \frac{4}{5} + \frac{2 i}{5}

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

[3 x = \frac{4}{5} - y = \frac{2}{5}]

[3 x = \frac{4}{5} - y = \frac{2}{5}] : x = \frac{4}{15}, y = - \frac{2}{5}

x = \frac{4}{15}, y = - \frac{2}{5}

\frac{z}{z + i} = 4

i (x - i y) = - i (x - i y)

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

z^{2} = 49 + i

z^{2} + (2 i - 3) z + 5 - 1 = 0

What is the answer to (x+iy)+2(x-iy)=(2i)/(1+2i) ?
The answer to (x+iy)+2(x-iy)=(2i)/(1+2i) is x= 4/15 ,y=-2/5