What is #2(cos330+isin330)#?

1 Answer
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+ib#:

enter image source here

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):

enter image source here

Which gives you the same position.

Hope it helps.