# What is 2(cos330+isin330)?

Feb 7, 2015

It is a Complex Number $z$ given in trigonometric form:
This complex number has a modulus of $2$ and an argument of 330° which help you to plot this particular number on a Complex Plane.
$i$ is the imaginary unit and represents $\sqrt{- 1}$.
These numbers are particularly useful when you want to solve a second degree equation which has a negative $\Delta$ (or discriminant) or in general when you have a problem involving negative square roots.
Each complex number can be plotted using either the trigonometric form (as in your case) or the corresponding rectangular form $a + i b$:

If you want to change your number into rectangular form you simply multiply $2$ times the quantities in bracket, giving:
2[cos(330°)+isin(330°)]=
2cos(330°)+2isin(330°)=
$= 1.732 - 1 i$
You can now plot again your complex number with $1.732$ on the REAL axis (Re) and $- 1$ on the IMMAGINARY axis (Im):

Which gives you the same position.

Hope it helps.