CPM Homework Help : A2C Problem 11-160

Compute the value of each expression below.

$( \frac { \sqrt { 2 } } { 2 } + \frac { i \sqrt { 2 } } { 2 } ) ^ { 2 }$
Hint (a):
$\frac{(2)}{4}+\frac{2i(2)}{4}+\frac{(-1)(2)}{4}$
Answer (a):
i

$( \frac { - \sqrt { 2 } } { 2 } - \frac { i \sqrt { 2 } } { 2 } ) ^ { 2 }$
Answer (b):
i

Use the results from parts (a) and (b) above to solve x² = i for x. (Find the square roots of i.)
Hint (c):
Notice that the expressions in parts (a) and (b), when squared, result in the value of i.
Locate $\frac { \sqrt { 2 } } { 2 } + i \frac { \sqrt { 2 } } { 2 }$ and $- \frac { \sqrt { 2 } } { 2 } - i \frac { \sqrt { 2 } } { 2 }$ on a set of complex axes. What do you notice about their locations?
Hint (d):