Question

Solve $x^4+9x^3+35x^2-x+4$=?, if $x=-5+\sqrt{-4}$

Answer 1

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

Since $x=-5+2i$

$x^2=25-4-10i$

$=21-10i$

$x^3=(21-10i)(-5+2i)$

$=-85+92i$

$x^4=441-100-420i$

$=341-420i$

Inserting values we set

$=341-420i+9(-85+92i)+35(21-10i)-21+10i+4$

$=341-765+735-21+4-420i+828i-350i+10i$

$=294-68i$