If $1-i$ is one of the zeroes of the polynomial $\mathrm{f}(z)=z^4-10z^2+az+b$, where

Question

If $1-i$ is one of the zeroes of the polynomial $\mathrm{f}(z)=z^4-10z^2+az+b$, where $a$ and $b$ are real, find the values of $a$ and $b$ and hence solve $\mathrm{f}(z)=0$.

Accepted Answer

$ a = 20, b = -16, z = 1 \pm i, -4, 2$.

Complex Numbers - Application of Conjugate Roots Theorem

Complex Numbers - Application of Conjugate Roots Theorem