Solve the equation z^2+z+1=0 using z=(x,y) and the basic definitions. (Hint: Note that y does not equal 0 because the equation X^2+X+1 does not equal 0 for any real number x.)
a. z1=--1+j(Sqrt3)/2 and z2=-1/2-j(Sqrt3)/2
b. z1=-1/2+j(Sqrt3)/2 and z2=-1/2-j(Sqrt3)/2
c. z1=-1/3+j(Sqrt3)/2 and z2=-j(Sqrt3)/2
d. z1=3/2+j(Sqrt3)/2 and z2=-1/2-j(Sqrt3)/4.
The solution lays out a neat series of calculations that will bring the reader to the correct answer from the options provided to solve a given equation involving complex numbers. There is also a little worded explanation to guide the reader through the steps.