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possible to write polynomial with degree 4 zeros 5, 1-i and 8i

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[tex](x-5)*(x-1)*(x+i)*(x-8i) \\ \\ (x^2-6x+5)*(x+i)*(x-8i) \\ \\ (x^3-ix^2-6x^2-6ix+5x+5i)*(x-8i) \\ \\ (x^3-(i+6)x^2-(6i-5)x+5i)*(x-8i) \\ \\ Polynomial:x^4-(6+9 i) x^3-(3-42 i) x^2-(48+35 i) x+40[/tex]
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