The question:

Suppose both c and $\displaystyle (1 + ic)^5$ are real (c != 0). Show that c = $\displaystyle \pm \sqrt{5 \pm 2\sqrt{5}}$

How do I solve this? I substituted the value of c into the complex number with the intent to find the magnitude and angle, but I'm not sure how to handle the $\displaystyle \pm$. Is it two different complex numbers? Am I attempting this correctly? Thanks.