Solve (2-mi)(3-ni)=8+4i

$$( 2 - m i ) ( 3 - n i ) = 8 + 4 i$$

Solve for m

$$m=\frac{2\left(-1-2i-in\right)}{n+3i}$$

$$n\neq -3i$$

Steps for Solving Linear Equation

Multiply -1 and i to get -i.

$$\left(2-im\right)\left(3-ni\right)=8+4i$$

Multiply -1 and i to get -i.

$$\left(2-im\right)\left(3-in\right)=8+4i$$

Use the distributive property to multiply 2-im by 3-in.

$$6-2in-3im-mn=8+4i$$

Subtract 6 from both sides.

$$-2in-3im-mn=8+4i-6$$

Subtract 6 from 8+4i to get 2+4i.

$$-2in-3im-mn=2+4i$$

Subtract -2in from both sides.

$$-3im-mn=2+4i-\left(-2in\right)$$

Combine all terms containing m.

$$\left(-3i-n\right)m=2+4i-\left(-2in\right)$$

The equation is in standard form.

$$\left(-3i-n\right)m=2in+\left(2+4i\right)$$

Divide both sides by -3i-n.

$$\frac{\left(-3i-n\right)m}{-3i-n}=\frac{2in+\left(2+4i\right)}{-3i-n}$$

Dividing by -3i-n undoes the multiplication by -3i-n.

$$m=\frac{2in+\left(2+4i\right)}{-3i-n}$$

Divide 2+4i+2in by -3i-n.

$$m=-\frac{2\left(in+\left(1+2i\right)\right)}{n+3i}$$

Solve for n

$$n=\frac{-2-4i-3im}{m+2i}$$

$$m\neq -2i$$

Steps for Solving Linear Equation

Multiply -1 and i to get -i.

$$\left(2-im\right)\left(3-ni\right)=8+4i$$

Multiply -1 and i to get -i.

$$\left(2-im\right)\left(3-in\right)=8+4i$$

Use the distributive property to multiply 2-im by 3-in.

$$6-2in-3im-mn=8+4i$$

Subtract 6 from both sides.

$$-2in-3im-mn=8+4i-6$$

Subtract 6 from 8+4i to get 2+4i.

$$-2in-3im-mn=2+4i$$

Subtract -3im from both sides.

$$-2in-mn=2+4i-\left(-3im\right)$$

Combine all terms containing n.

$$\left(-2i-m\right)n=2+4i-\left(-3im\right)$$

The equation is in standard form.

$$\left(-2i-m\right)n=3im+\left(2+4i\right)$$

Divide both sides by -2i-m.

$$\frac{\left(-2i-m\right)n}{-2i-m}=\frac{3im+\left(2+4i\right)}{-2i-m}$$

Dividing by -2i-m undoes the multiplication by -2i-m.

$$n=\frac{3im+\left(2+4i\right)}{-2i-m}$$

Divide 2+4i+3im by -2i-m.

$$n=-\frac{3im+\left(2+4i\right)}{m+2i}$$