Three identical charges (q = -5.0 x10^(-6) C) lie along a circle of radius 2.0 m at angles of 30°, 150°, and 270°, as shown in Figure. What is the resultant electric field at the center of the circle?

Problem Solution

The quick answer to this problem at simple view is ZERO. Right now your brain is in confusion state because can't understand why is to easy know the answer at simple view?.
But, our work is explain this! get ready? well let's get started!
the first step to solve this is convert all angles to 0°- 90° scale so:

Now, remember that positive electric charge have an divergent electric field as shown in this image

therefore, our electric fields look as follow:

Using the fact that all electric charges are the same in magnitude, so all electric fields are equals in magnitude. With this we can write the equations for vertical an horizontal components of net electric field at center of circle as:

having as final result :

as you can see... in words of Guns N' Roses.. it's so easy!