Solve (z-2)i=a+i

$$( z - 2 ) i = a + i$$

Solve for a

$$a=iz-3i$$

Solution Steps

Use the distributive property to multiply z-2 by i.

$$iz-2i=a+i$$

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

$$a+i=iz-2i$$

Subtract i from both sides.

$$a=iz-2i-i$$

Subtract i from -2i to get -3i.

$$a=iz-3i$$

Solve for z

$$z=3-ia$$

Steps for Solving Linear Equation

Use the distributive property to multiply z-2 by i.

$$iz-2i=a+i$$

Add 2i to both sides.

$$iz=a+i+2i$$

Add i and 2i to get 3i.

$$iz=a+3i$$

Divide both sides by i.

$$\frac{iz}{i}=\frac{a+3i}{i}$$

Dividing by i undoes the multiplication by i.

$$z=\frac{a+3i}{i}$$

Divide a+3i by i.

$$z=3-ia$$