Resolver frac{x+2ysqrt{-1}}{2-sqrt{-1}}+frac{2x+ysqrt{-1}}{2+sqrt{-1}}=23/5

$$\frac{ x+2y \sqrt{ -1 } }{ 2- \sqrt{ -1 } } + \frac{ 2x+y \sqrt{ -1 } }{ 2+ \sqrt{ -1 } } = \frac{ 23 }{ 5 }$$

Resolva para y

$$y=\left(\frac{12}{37}+\frac{35}{37}i\right)x+\left(-\frac{23}{37}-\frac{138}{37}i\right)$$

Passos Para Resolver Uma Equação Linear

Calcule a raiz quadrada de -1 e obtenha i.

$$\frac{x+2yi}{2-\sqrt{-1}}+\frac{2x+y\sqrt{-1}}{2+\sqrt{-1}}=\frac{23}{5}$$

Multiplique 2 e i para obter 2i.

$$\frac{x+2iy}{2-\sqrt{-1}}+\frac{2x+y\sqrt{-1}}{2+\sqrt{-1}}=\frac{23}{5}$$

Calcule a raiz quadrada de -1 e obtenha i.

$$\frac{x+2iy}{2-i}+\frac{2x+y\sqrt{-1}}{2+\sqrt{-1}}=\frac{23}{5}$$

Calcule a raiz quadrada de -1 e obtenha i.

$$\frac{x+2iy}{2-i}+\frac{2x+yi}{2+\sqrt{-1}}=\frac{23}{5}$$

Calcule a raiz quadrada de -1 e obtenha i.

$$\frac{x+2iy}{2-i}+\frac{2x+yi}{2+i}=\frac{23}{5}$$

Divida cada termo de x+2iy por 2-i para obter \frac{x}{2-i}+\frac{2iy}{2-i}.

$$\frac{x}{2-i}+\frac{2iy}{2-i}+\frac{2x+yi}{2+i}=\frac{23}{5}$$

Dividir 2iy por 2-i para obter \left(-\frac{2}{5}+\frac{4}{5}i\right)y.

$$\frac{x}{2-i}+\left(-\frac{2}{5}+\frac{4}{5}i\right)y+\frac{2x+yi}{2+i}=\frac{23}{5}$$

Divida cada termo de 2x+yi por 2+i para obter \frac{2x}{2+i}+\frac{yi}{2+i}.

$$\frac{x}{2-i}+\left(-\frac{2}{5}+\frac{4}{5}i\right)y+\frac{2x}{2+i}+\frac{yi}{2+i}=\frac{23}{5}$$

Dividir 2x por 2+i para obter \left(\frac{4}{5}-\frac{2}{5}i\right)x.

$$\frac{x}{2-i}+\left(-\frac{2}{5}+\frac{4}{5}i\right)y+\left(\frac{4}{5}-\frac{2}{5}i\right)x+\frac{yi}{2+i}=\frac{23}{5}$$

Dividir yi por 2+i para obter y\left(\frac{1}{5}+\frac{2}{5}i\right).

$$\frac{x}{2-i}+\left(-\frac{2}{5}+\frac{4}{5}i\right)y+\left(\frac{4}{5}-\frac{2}{5}i\right)x+y\left(\frac{1}{5}+\frac{2}{5}i\right)=\frac{23}{5}$$

Combine \left(-\frac{2}{5}+\frac{4}{5}i\right)y e y\left(\frac{1}{5}+\frac{2}{5}i\right) para obter \left(-\frac{1}{5}+\frac{6}{5}i\right)y.

$$\frac{x}{2-i}+\left(-\frac{1}{5}+\frac{6}{5}i\right)y+\left(\frac{4}{5}-\frac{2}{5}i\right)x=\frac{23}{5}$$

Subtraia \frac{x}{2-i} de ambos os lados.

$$\left(-\frac{1}{5}+\frac{6}{5}i\right)y+\left(\frac{4}{5}-\frac{2}{5}i\right)x=\frac{23}{5}-\frac{x}{2-i}$$

Subtraia \left(\frac{4}{5}-\frac{2}{5}i\right)x de ambos os lados.

$$\left(-\frac{1}{5}+\frac{6}{5}i\right)y=\frac{23}{5}-\frac{x}{2-i}-\left(\frac{4}{5}-\frac{2}{5}i\right)x$$

Multiplique -1 e \frac{4}{5}-\frac{2}{5}i para obter -\frac{4}{5}+\frac{2}{5}i.

$$\left(-\frac{1}{5}+\frac{6}{5}i\right)y=\frac{23}{5}-\frac{x}{2-i}+\left(-\frac{4}{5}+\frac{2}{5}i\right)x$$

A equação está no formato padrão.

$$\left(-\frac{1}{5}+\frac{6}{5}i\right)y=\left(-\frac{6}{5}+\frac{1}{5}i\right)x+\frac{23}{5}$$

Divida ambos os lados por -\frac{1}{5}+\frac{6}{5}i.

$$\frac{\left(-\frac{1}{5}+\frac{6}{5}i\right)y}{-\frac{1}{5}+\frac{6}{5}i}=\frac{\left(-\frac{6}{5}+\frac{1}{5}i\right)x+\frac{23}{5}}{-\frac{1}{5}+\frac{6}{5}i}$$

Dividir por -\frac{1}{5}+\frac{6}{5}i anula a multiplicação por -\frac{1}{5}+\frac{6}{5}i.

$$y=\frac{\left(-\frac{6}{5}+\frac{1}{5}i\right)x+\frac{23}{5}}{-\frac{1}{5}+\frac{6}{5}i}$$

Divida \frac{23}{5}+\left(-\frac{6}{5}+\frac{1}{5}i\right)x por -\frac{1}{5}+\frac{6}{5}i.

$$y=\left(\frac{12}{37}+\frac{35}{37}i\right)x+\left(-\frac{23}{37}-\frac{138}{37}i\right)$$

Resolva para x

$$x=\left(\frac{12}{37}-\frac{35}{37}i\right)y+\left(\frac{138}{37}+\frac{23}{37}i\right)$$