Complex Numbers

Prove that 1+i is a root of equation z^4+3z^2-6z+10=0. Find all the other roots.

By substituting (1+i) instead of z and checking if it equals zero.

Indeed that is a way of checking whether it is a root. Then you should be able to find another root related to this one because the coefficients of the polynomial are real. Once you have the other root you can deduce the quartic into a product of 2 linear and 1 quadratic polynomials and solve the quadratic as usual to get your 2 last roots.