Ask Me Help Desk - Complex numbers equation

We can factor just like we would a regular old quadratic.

$x^{4}-(5-2i)x^{2}-10i=0$

What two numbers when multiplied equal -10i and when added equal -5+2i?

How about 2i and -5?

$x^{4}+2ix^{2}-5x^{2}-10i$

Group and factor

$x^{2}(x^{2}+2i)-5(x^{2}+2i)$

$(x^{2}-5)(x^{2}+2i)=0$

What values of x make

$x^{2}-5=0$ ?

Difference of two squares:

$(x+\sqrt{5})(x-\sqrt{5})=0$

What values of x make

$x^{2}+2i=0$ ?

Factor:

$(x-(1-i))(x+(1-i))=0$