Question 6614
You believe that anything divided by itself = 1, right? And multiplying something by 1 doesn't change the original value?


We'll multiply both numerator and denominator with the denominator's conjugate. The conjugate is exactly the complex number a +/- bi EXCEPT that you flip the sign before the bi term. Since you've got 3 + i, the conjugate would be 3 - i. We'll multiply both numerator and denominator by the conjugate.


{{{ ((1 - 2i)/(3+i))*((3-i)/(3-i)) }}} really is multiplying your original rational expression by 1, so it doesn't change anything. This is just a trick you can use.


Let's take care of the numerator first by performing FOIL:


{{{ (1 - 2i)(3 - i) = 3 - i - 6i + 2i^2 = 3 - 7i - 2 = 1 - 7i }}}


Let's take the denominator and do FOIL


{{{ (3 + i)(3 - i) = 9 - 3i + 3i - (-1) = 10 }}}


So, numerator over denominator would give you {{{ (1 - 7i)/10 }}}. They want it in a + bi form. Remember your fraction rule that says {{{ (a - b)/c = a/c - a/b }}}. So in this case, your answer will be {{{ 1/10 - (7/10)i }}}