2
$\begingroup$

I can't seem to find the solutions to $z^4+1=0 $. $z$ is in the complex plane.

The solutions show four roots; however, how do I find them once $z^4 = -1$?

  • 2
    Can you find one? Do you know geometrically (in *polar coordinates*) what happens to a complex number $z$ when raised to power $n$? In the solution, basically you will draw a square in the unit circle.2012-11-29
  • 0
    http://math.stackexchange.com/questions/241206/find-all-complex-numbers-z-satisfying-the-equation/2012-11-29
  • 0
    Do you know the magic factorization $z^4+4=(z^2-2z+2)(z^2+2z+2)$? From this you can get what you’re seeking.2012-11-29
  • 0
    Note: I think it is more appropriate to say "find the *solutions* to $X$" when $X$ is an equation; and "find the *roots* of $X$" when $X$ is a polynomial.2012-11-29

6 Answers 6