#### Answer

The two square roots are:
$cos~0^{\circ}+i~sin~0^{\circ}$
$cos~180^{\circ}+i~sin~180^{\circ}$
We can graph the two square roots in the complex plane:

#### Work Step by Step

$z = 1 + 0~i$
$z = cos~0^{\circ}+i~sin~0^{\circ}$
$r = 1$ and $\theta = 0^{\circ}$
We can use this equation to find the square roots:
$z^{1/n} = r^{1/n}~[cos(\frac{\theta}{n}+\frac{360^{\circ}~k}{n})+i~sin(\frac{\theta}{n}+\frac{360^{\circ}~k}{n})]$, where $k \in \{0, 1, 2,...,n-1\}$
When k = 0:
$z^{1/2} = 1^{1/2}~[cos(\frac{0^{\circ}}{2}+\frac{(360^{\circ})(0)}{2})+i~sin(\frac{0^{\circ}}{2}+\frac{(360^{\circ})(0)}{2})]$
$z^{1/2} = 1~[cos~0^{\circ}+i~sin~0^{\circ}]$
$z^{1/2} = cos~0^{\circ}+i~sin~0^{\circ}$
When k = 1:
$z^{1/2} = 1^{1/2}~[cos(\frac{0^{\circ}}{2}+\frac{(360^{\circ})(1)}{2})+i~sin(\frac{0^{\circ}}{2}+\frac{(360^{\circ})(1)}{2})]$
$z^{1/2} = 1~[cos~180^{\circ}+i~sin~180^{\circ}]$
$z^{1/2} = cos~180^{\circ}+i~sin~180^{\circ}$
We can graph the two square roots in the complex plane: