Answer
The first three tenth roots of 1 are:
1
$0.809+0.588~i$
$0.309+0.951~i$
Work Step by Step
We can find the first three tenth roots of 1:
$\theta = 0^{\circ}$:
$1^{1/10} = cos~\theta^{\circ}+i~sin~\theta^{\circ}$
$1^{1/10} = cos~0^{\circ}+i~sin~0^{\circ}$
$1^{1/10} = 1+0i$
$\theta = 36^{\circ}$:
$1^{1/10} = cos~\theta^{\circ}+i~sin~\theta^{\circ}$
$1^{1/10} = cos~36^{\circ}+i~sin~36^{\circ}$
$1^{1/10} = 0.809+0.588~i$
$\theta = 72^{\circ}$:
$1^{1/10} = cos~\theta^{\circ}+i~sin~\theta^{\circ}$
$1^{1/10} = cos~72^{\circ}+i~sin~72^{\circ}$
$1^{1/10} = 0.309+0.951~i$
