### Home > A2C > Chapter 11 > Lesson 11.3.3 > Problem11-160

11-160.

Compute the value of each expression below.

1. $( \frac { \sqrt { 2 } } { 2 } + \frac { i \sqrt { 2 } } { 2 } ) ^ { 2 }$

$\frac{(2)}{4}+\frac{2i(2)}{4}+\frac{(-1)(2)}{4}$

i

1. $( \frac { - \sqrt { 2 } } { 2 } - \frac { i \sqrt { 2 } } { 2 } ) ^ { 2 }$

i

1. Use the results from parts (a) and (b) above to solve x2 = i for x. (Find the square roots of i.)

Notice that the expressions in parts (a) and (b), when squared, result in the value of i.

2. 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?