Division with remainder (polynomials)/C/(5+i)x^4+ix^2+(3-2i)x-1/x^2+ix+3-i/Exercise

Perform, in the polynomial ring ${}\mathbb {C} [X]$, the division with remainder ${}{\frac {P}{T}}$, where

${}P=(5+X^{2}+{\mathrm {i} }X+3-{\mathrm {i} })X^{4}+X^{2}+{\mathrm {i} }X+3-{\mathrm {i} }X^{2}+(3-2X^{2}+{\mathrm {i} }X+3-{\mathrm {i} })X-1\,$

and

${}T=X^{2}+{\mathrm {i} }X+3-{\mathrm {i} }\,.$

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