Consider the difference quotient formula.

Evaluate the function at .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Add and .

Reorder and .

Add and .

The final answer is .

Reorder.

Move .

Reorder and .

Find the components of the definition.

Plug in the components.

Simplify the numerator.

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Subtract from .

Add and .

Add and .

Add and .

Subtract from .

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Find the Difference Quotient f(z)=z^2-3+2i