Solve the equation $x^7- 2ix^4 - ix^3 -2 = 0$ for $x$

Question

I am having difficulty factorising the equation.

Answer 1

Hint. You can collect $(x^4-i)$: $$x^7- 2ix^4 - ix^3 -2=x^3(x^4-i)- 2i(x^4-i)=(x^4-i)(x^3-2i).$$ Can you take it from here?

Answer 2

$$x^7-ix^3-2ix^4-2=0\\(x^7-ix^3)-2(ix^4+1)=0\\ x^3(x^4-i)-2(ix^4+1)=0\\\frac{i}{i}x^3(x^4-i)-2(ix^4+1)=0\\ \frac{1}{i}x^3(ix^4-i^2)-2(ix^4+1)=0\\ \frac{1}{i}x^3(ix^4+1)-2(ix^4+1)=0\\ (\frac{x^3}{i}-2)(ix^4+1)=0\\ (\frac{x^3-2i}{i})(ix^4+1)=0\\ \to (x^3-2i)(ix^4+1)=0\\$$