can anyone solve this complex equation?

Question

$iz^6 + 2z^2 -2i = 0$

i'm really out of ideas. please help me.

Answer 1

Substitute $z^2=u$ and solve for $u$ using Cardano's formula for cubic polynomials.

https://en.m.wikipedia.org/wiki/Cubic_equation

Than take the two roots of each of the tree solutions.

Then, compare what you got to the results wolframalpha gives you.