# How do you find the standard notation of 5(cos 210+isin210)?

Feb 7, 2015

I suppose you want this complex number in the $a + i b$ form.

You have only to evaluate your $\cos$ and $\sin$ and do the nultiplication by 5:

5[cos(210°)+isin(210°)]=
=5cos(210°)+5isin(210°)=
$= 5 \left(- \frac{\sqrt{3}}{2}\right) + 5 i \left(- \frac{1}{2}\right) =$
$= - 5 \frac{\sqrt{3}}{2} - \frac{5}{2} i$

Which is in the form: $a + i b$

If you want you can evaluate the square root and the divisions but I would leave it like it is.

hope it helps