Rewrite each of the following in simplest complex or radical form.

1. $\frac { \sqrt { 2 } + \sqrt { 2 } i } { \sqrt { 2 } - \sqrt { 2 } i }$

   Step 1(a):

   $\text{Factor out the }\sqrt{2}\text{ and simplify.}$

   $\frac{1+i}{1-i}$

   Step 2(a):

   Multiply by the conjugate of the denominator.

   $\frac{(1+i)(1+i)}{(1-i)(1+i)}$

   Answer (a):

   i

2. The reciprocal of $\frac { 1 } { 2 } + \frac { \sqrt { 5 } } { 2 }$

   Hint (b):

   See part (a).