Solve 2ix-y=(3-2i)(1+i)/i(1+2i)

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

Solve for x

$$x=-\frac{iy}{2}+\left(-\frac{7}{10}+\frac{9}{10}i\right)$$

Steps for Solving Linear Equation

Multiply 3-2i and 1+i to get 5+i.

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

Multiply i and 1+2i to get -2+i.

$$2ix-y=\frac{5+i}{-2+i}$$

Multiply both numerator and denominator of \frac{5+i}{-2+i} by the complex conjugate of the denominator, -2-i.

$$2ix-y=\frac{\left(5+i\right)\left(-2-i\right)}{\left(-2+i\right)\left(-2-i\right)}$$

Do the multiplications in \frac{\left(5+i\right)\left(-2-i\right)}{\left(-2+i\right)\left(-2-i\right)}.

$$2ix-y=\frac{-9-7i}{5}$$

Divide -9-7i by 5 to get -\frac{9}{5}-\frac{7}{5}i.

$$2ix-y=-\frac{9}{5}-\frac{7}{5}i$$

Add y to both sides.

$$2ix=-\frac{9}{5}-\frac{7}{5}i+y$$

The equation is in standard form.

$$2ix=y+\left(-\frac{9}{5}-\frac{7}{5}i\right)$$

Divide both sides by 2i.

$$\frac{2ix}{2i}=\frac{y+\left(-\frac{9}{5}-\frac{7}{5}i\right)}{2i}$$

Dividing by 2i undoes the multiplication by 2i.

$$x=\frac{y+\left(-\frac{9}{5}-\frac{7}{5}i\right)}{2i}$$

Divide -\frac{9}{5}-\frac{7}{5}i+y by 2i.

$$x=-\frac{iy}{2}+\left(-\frac{7}{10}+\frac{9}{10}i\right)$$

Solve for y

$$y=2ix+\left(\frac{9}{5}+\frac{7}{5}i\right)$$

Steps for Solving Linear Equation

Multiply 3-2i and 1+i to get 5+i.

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

Multiply i and 1+2i to get -2+i.

$$2ix-y=\frac{5+i}{-2+i}$$

Multiply both numerator and denominator of \frac{5+i}{-2+i} by the complex conjugate of the denominator, -2-i.

$$2ix-y=\frac{\left(5+i\right)\left(-2-i\right)}{\left(-2+i\right)\left(-2-i\right)}$$

Do the multiplications in \frac{\left(5+i\right)\left(-2-i\right)}{\left(-2+i\right)\left(-2-i\right)}.

$$2ix-y=\frac{-9-7i}{5}$$

Divide -9-7i by 5 to get -\frac{9}{5}-\frac{7}{5}i.

$$2ix-y=-\frac{9}{5}-\frac{7}{5}i$$

Subtract 2ix from both sides.

$$-y=-\frac{9}{5}-\frac{7}{5}i-2ix$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{-\frac{9}{5}-\frac{7}{5}i-2ix}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{-\frac{9}{5}-\frac{7}{5}i-2ix}{-1}$$

Divide -\frac{9}{5}-\frac{7}{5}i-2ix by -1.

$$y=2ix+\left(\frac{9}{5}+\frac{7}{5}i\right)$$