Solve i+m/n:(1/2)^-2-sqrt{16}=0

$$i + \frac { m } { n } : ( \frac { 1 } { 2 } ) ^ { - 2 } - \sqrt { 16 } = 0$$

Solve for m

$$m=\left(16-4i\right)n$$

$$n\neq 0$$

Solution Steps

Calculate \frac{1}{2} to the power of -2 and get 4.

$$i+\frac{\frac{m}{n}}{4}-\sqrt{16}=0$$

Calculate the square root of 16 and get 4.

$$i+\frac{\frac{m}{n}}{4}-4=0$$

Subtract i from both sides. Anything subtracted from zero gives its negation.

$$\frac{\frac{m}{n}}{4}-4=-i$$

Add 4 to both sides.

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

Multiply both sides of the equation by 4.

$$\frac{m}{n}=-4i+16$$

Multiply both sides of the equation by n.

$$m=n\times \left(-4i\right)+n\times 16$$

Combine n\times \left(-4i\right) and n\times 16 to get \left(16-4i\right)n.

$$m=\left(16-4i\right)n$$

Solve for n

$$n=\left(\frac{1}{17}+\frac{1}{68}i\right)m$$

$$m\neq 0$$

Steps for Solving Linear Equation

Calculate \frac{1}{2} to the power of -2 and get 4.

$$i+\frac{\frac{m}{n}}{4}-\sqrt{16}=0$$

Calculate the square root of 16 and get 4.

$$i+\frac{\frac{m}{n}}{4}-4=0$$

Subtract i from both sides. Anything subtracted from zero gives its negation.

$$\frac{\frac{m}{n}}{4}-4=-i$$

Add 4 to both sides.

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

Multiply both sides of the equation by 4.

$$\frac{m}{n}=-4i+16$$

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$m=n\times \left(-4i\right)+n\times 16$$

Combine n\times \left(-4i\right) and n\times 16 to get \left(16-4i\right)n.

$$m=\left(16-4i\right)n$$

Swap sides so that all variable terms are on the left hand side.

$$\left(16-4i\right)n=m$$

Divide both sides by 16-4i.

$$\frac{\left(16-4i\right)n}{16-4i}=\frac{m}{16-4i}$$

Dividing by 16-4i undoes the multiplication by 16-4i.

$$n=\frac{m}{16-4i}$$

Divide m by 16-4i.

$$n=\left(\frac{1}{17}+\frac{1}{68}i\right)m$$

Variable n cannot be equal to 0.

$$n=\left(\frac{1}{17}+\frac{1}{68}i\right)m\text{, }n\neq 0$$