How do you write a polynomial equation of least degree given the roots 6, 2i, -2i, i, -i?

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How do you write a polynomial equation of least degree given the roots 6, 2i, -2i, i, -i?

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Answer 1 · 2017-04-23T04:15:37

#z^5-6z^4+5z^3-30z^2+4z-24=0#

Explanation:

#(z-6)(z-2i)(z-(-2i))(z-i)(z-(-i))=0#
#(z-6)(z-2i)(z+2i)(z-i)(z+i)=0#
#(z-6)(z^2-2zi+2zi-4i^2)(z^2-zi+zi-i^2)=0#
#(z-6)(z^2+4)(z^2+1)=0#
#(z-6)(z^4+4z^2+z^2+4)=0#
#(z-6)(z^4+5z^2+4)=0#
#z^5-6z^4+5z^3-30z^2+4z-24=0#

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How do you write a polynomial equation of least degree given the roots 6, 2i, -2i, i, -i?

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