Determine whether the following equations have a solution or not? Justify your answer. ?

Question

z^2 + z + 1 = 0

Please show me how to work this problem.

Answer 1

i don't think it does cause you can't factor and if you do the quadratic formula you'll end up with a negative number under the radical sign, which means an imaginary number. there's no real answers to the problem, therefore, no solution. imaginary numbers are just that, imaginary.