Simplifying a Complex Fraction

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

To simplify a quotient of 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 conjugate is eight minus two i.

Now let's expand the numerator: three times eight is twenty-four, three times negative two i is negative six i, negative five i times eight is negative forty i, and negative five i times negative two i is positive ten i squared.

Since i squared equals negative one, ten i squared becomes negative ten.

Combining the real terms, twenty-four minus ten equals fourteen. So the numerator is fourteen minus forty-six i.