Simplifying a Complex Number Quotient

Hi Destiny, let's solve this complex number division together.

To simplify the quotient of two complex numbers, we multiply the numerator and the denominator by the complex conjugate of the denominator.

The denominator is eight plus two i, so its complex conjugate is eight minus two i. We multiply by one in the form of this conjugate over itself.

Let's expand the denominator first using the difference of squares pattern. Since i squared equals negative one, eight squared minus two i squared becomes sixty-four plus four.

Now, let's expand the numerator by distributing the terms: three times eight, three times negative two i, negative five i times eight, and negative five i times negative two i.