Question

How do I make a polynomial out of an equation that is
Second degree; 2i
(main question: how do I make a polynomial out of imaginary numbers?)

Example of a solved one:
Second dregree; 3 = x^2-6x+9

Answer 1

start with
\[(x-2i)(x+2i)\] then multiply

Answer 2

get
\[x^2+4\] pretty much in your head

Answer 3

think "if the solution is 2i, then it must have been
\[x^2=-4\]

Answer 4

x = 2i or x = -2i .... note: complex solutions come in conjugate pairs


x-2i = 0 or x+2i = 0


(x-2i)(x+2i) = 0


x^2-4i^2 = 0


x^2 - 4(-1) = 0


x^2 + 4 = 0


So the polynomial x^2 + 4 has the roots 2i and -2i

Answer 5

Thanks.