Solve (1+i)*(x+iy)*(4-2i)=7*5i

$$( 1 + i ) \cdot ( x + i y ) \cdot ( 4 - 2 i ) = 7 \cdot 5 i$$

Solve for x

$$x=\frac{7}{4}+\frac{21}{4}i-iy$$

Steps for Solving Linear Equation

Multiply 1+i and 4-2i to get 6+2i.

$$\left(6+2i\right)\left(x+iy\right)=7\times \left(5i\right)$$

Use the distributive property to multiply 6+2i by x+iy.

$$\left(6+2i\right)x+\left(-2+6i\right)y=7\times \left(5i\right)$$

Multiply 7 and 5i to get 35i.

$$\left(6+2i\right)x+\left(-2+6i\right)y=35i$$

Subtract \left(-2+6i\right)y from both sides.

$$\left(6+2i\right)x=35i-\left(-2+6i\right)y$$

Multiply -1 and -2+6i to get 2-6i.

$$\left(6+2i\right)x=35i+\left(2-6i\right)y$$

The equation is in standard form.

$$\left(6+2i\right)x=\left(2-6i\right)y+35i$$

Divide both sides by 6+2i.

$$\frac{\left(6+2i\right)x}{6+2i}=\frac{\left(2-6i\right)y+35i}{6+2i}$$

Dividing by 6+2i undoes the multiplication by 6+2i.

$$x=\frac{\left(2-6i\right)y+35i}{6+2i}$$

Divide 35i+\left(2-6i\right)y by 6+2i.

$$x=\frac{7}{4}+\frac{21}{4}i-iy$$

Solve for y

$$y=ix+\left(\frac{21}{4}-\frac{7}{4}i\right)$$

Steps for Solving Linear Equation

Multiply 1+i and 4-2i to get 6+2i.

$$\left(6+2i\right)\left(x+iy\right)=7\times \left(5i\right)$$

Use the distributive property to multiply 6+2i by x+iy.

$$\left(6+2i\right)x+\left(-2+6i\right)y=7\times \left(5i\right)$$

Multiply 7 and 5i to get 35i.

$$\left(6+2i\right)x+\left(-2+6i\right)y=35i$$

Subtract \left(6+2i\right)x from both sides.

$$\left(-2+6i\right)y=35i-\left(6+2i\right)x$$

Multiply -1 and 6+2i to get -6-2i.

$$\left(-2+6i\right)y=35i+\left(-6-2i\right)x$$

The equation is in standard form.

$$\left(-2+6i\right)y=\left(-6-2i\right)x+35i$$

Divide both sides by -2+6i.

$$\frac{\left(-2+6i\right)y}{-2+6i}=\frac{\left(-6-2i\right)x+35i}{-2+6i}$$

Dividing by -2+6i undoes the multiplication by -2+6i.

$$y=\frac{\left(-6-2i\right)x+35i}{-2+6i}$$

Divide 35i+\left(-6-2i\right)x by -2+6i.

$$y=ix+\left(\frac{21}{4}-\frac{7}{4}i\right)$$