Question

Write the complex number in the form a + bi.

5/2(cos 150° + i sin 150°)

Answer 1

\(\bf r[cos(\theta)+i\ sin(\theta)]\to (r,\theta)\) what do you think the coordinates will be there? that is, what's "r" and what is the angle?

Answer 2

ooh so 5/2+150i ?

Answer 3

anyhow... once you find that, keep in mind that \(\large \begin{cases}
cos(\theta)=\frac{x}{r}\to rcos(\theta)={\color{blue}{ x}}
\\ \quad \\
sin(\theta)=\frac{y}{r}\to rsin(\theta)={\color{blue}{ y}}
\end{cases}\)

Answer 4

and that'd give the (x,y) rectangular coordinates...which can be written as x + yi

Answer 5

and yes... the r = 5/2 and the angle is 150 degrees
so get "x" and "y" :)

Answer 6

$$
\cfrac{5}{2}\left (\cos 150 + i\sin 150\right )=\cfrac{5}{2}\left (\cfrac{-\sqrt 3}{2}+i\cfrac{1}{2}\right )\\
=-\cfrac{5\sqrt 3}{4}+\cfrac{5}{4}=5\cfrac{1-\sqrt 3}{4}
$$
Does this make sense?