Question

If $x=-5+2\sqrt{-4},$ find the value of $x^4+9x^3+35x^2-x+4$ .

Answer 1

$x^4+9x^3+35x^2-x+4$

$x=-5+2\sqrt{-4}$

${(-5+2\sqrt{-4})}^4+9{(-5+2\sqrt{-4})}^3+35{(-5+2\sqrt{-4})}^2-(-5+2\sqrt{-4})+4$

$=-1519-720i+9(115+236i)+35(9-40i)-(-5+4i)+4$

$=-1519-720i+1035+2124i+315-1400i+5-4i+4$

$=-720i+2124i-1400i-4i-1519+1035+315+5+4$

$=-1519+1035+315+5+4$

$=-160$