Question

What is `2(cos330+isin330)`?

Answer 1

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+ib`:

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°)=`
`=1.732-1i`
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.