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 - Applying the Conjugate Root Theorem

Complex Numbers - Applying the Conjugate Root Theorem

Solution:

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