An algebra problem by Nick Okita

Algebra Level 4

Consider the complex polynomial \[p(z) = z^{4} + az^{3} + 5z^{2} - iz - 6\], where a is a complex constant. It's known that 2i is a root of \[p(z) = 0\], the other three roots are:

This question was taken from ITA (Instituto Tecnológico da Aeronáutica) Brazil 2013-2014 entrance exam.

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