Standard +0.3 This is a straightforward application of the complex conjugate root theorem for polynomials with real coefficients. Students must recognize that if i and 2-i are roots, then -i and 2+i must also be roots, then expand (z-i)(z+i)(z-(2-i))(z-(2+i)) to find coefficients. The algebra is routine with no conceptual challenges beyond the standard theorem.
7.
In the quartic equation \(z ^ { 4 } + a z ^ { 3 } + b z ^ { 2 } + c z + d = 0\), the coefficients \(a , b , c\) and \(d\) are real. Two of the roots of the equation are i and \(2 - \mathrm { i }\).
Find the value of \(a , b , c\) and \(d\). [0pt]
7.
In the quartic equation $z ^ { 4 } + a z ^ { 3 } + b z ^ { 2 } + c z + d = 0$, the coefficients $a , b , c$ and $d$ are real. Two of the roots of the equation are i and $2 - \mathrm { i }$.
Find the value of $a , b , c$ and $d$.\\[0pt]
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