Notice that pi/6 radians are equal to 30°; on the other hand, 30° is an inner angle of the triangle shown below
Thus, from the diagram above,
[tex]\begin{gathered} \Rightarrow sin(30\degree)=sin(\frac{\pi}{6})=\frac{\frac{1}{2}}{1}=\frac{1}{2} \\ and \\ cos(30\degree)=cos(\frac{\pi}{6})=\frac{\frac{\sqrt{3}}{2}}{1}=\frac{\sqrt{3}}{2} \end{gathered}[/tex]
Therefore, finding z,
[tex]\Rightarrow z=\frac{\sqrt{3}}{2}+\frac{1}{2}*i[/tex]
The answer is sqrt(3)/2+i/2
