I don't understand how to find zeros of a function (with imaginary numbers)

My math problem says:
2i is a zero of P(x) = x^3-2ix^2-4x+8i. Find the other zeros of P.
I don't understand how to do this, and what to do with the imaginary numbers. Please help walk me through it? This chapter confuses me so much. Thanks!

since 2i is a zero then its reprsentation is (x - 2i). now we can do division


..............x^2.............- 4
..............x^3 - 2ix^2 - 4x + 8i
x - 2i......x^3 - 2ix^2
................................- 4x + 8i
................................- 4x + 8i

so the other factor is x^2 - 4

x^2 - 4

(x - 2)(x + 2)

so the other zeros are 2 and - 2

Simply the zero for the Complex set is:

0 + 0i

It means you must group by the part, real and the part, imaginary.

HINT:
(x^3 - 4x ) + ( 8 - 2 x^2 ) i = 0 + 0 i
Thus
x ( x^2 - 4 ) + 2 ( 4 - x^2) i = 0 + 0 i

R = 0
I i = 0 i

Intersect same values from the both part sets (real and imaginary)
and solve.

Ans. x = - 2 and x = 2

:)

factorise --->P(x) = (x-2i)(x+2)(x-2) = 0 ---> x = ...