Question

Write the following complex number in standard form, z = a + bi. Write the exact answer. Do not round.cos(#) + isin(%)

Answer 1

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,

`\begin{gathered} \Rightarrow sin(30\degree)=sin((\pi)/(6))=((1)/(2))/(1)=(1)/(2) \\ and \\ cos(30\degree)=cos((\pi)/(6))=((√(3))/(2))/(1)=(√(3))/(2) \end{gathered}`

Therefore, finding z,

`\Rightarrow z=(√(3))/(2)+(1)/(2)*i`

The answer is sqrt(3)/2+i/2