# Evaluate (9+i)/(9-i)

Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Multiply.
Combine.
Simplify the numerator.
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 .
Move to the left of .
Multiply .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Subtract from .
Simplify the denominator.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Subtract from .
Simplify each term.
Rewrite as .
Multiply by .
Cancel the common factor of and .
Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Split the fraction into two fractions.
Evaluate (9+i)/(9-i)