This problem can be solved very similarly to a binomial such as . In this case, both the real and nonreal terms in the complex number are eligible to be divided by the real divisor.

, so

First, divide 100 by as follows:

Now, divide this by :

First, divide 100 by as follows:

Now dvide this result by :

Solving this problem using a conjugate is just like conjugating a binomial to simplify a denominator.

Multiply both terms by the denominator's conjugate.

Simplify. Note .

Combine and simplify.

Simplify the numerator.

The prime denominator prevents further simplifying.

Thus, .

Multiply both numberator and denominator by :

First, evaluate :

Now divide this into :

First, evaluate using the square pattern:

Divide this into :

This problem can be solved in a way similar to other kinds of division problems (with binomials, for example). We need to get the imaginary number out of the denominator, so we will multiply the denominator by its conjugate and multiply the top by it as well to preserve the number's value.

Then, recall by definition, so we can simplify this further:

This is as far as we can simplify, so it is our final answer.