z^4+4z^2-z+6=0 is correct
then
https://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php
Find the four complex roots of (z^2 + 2)^2 + 2 = z
I expanded it and got z^4+4z^2-z+6=0, not sure where to go from here
2 answers
note quartic method there
https://www.mathportal.org/formulas/algebra/solalgebric.php
https://www.mathportal.org/formulas/algebra/solalgebric.php