Question

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

• A. 160
• B. -160
• C. 60
• D. -60

Answer 1

The correct option is B -160

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

$x=-5+4i$

$x^2=25+16i^2-40i$

$=25-16-40i$

$x^2=9-40i$

$x^3=(9-40i)(-5+4i)$

$=-45+36i+200i-160i^2$

$=160-45+236i$

$x^3=115+236i$

$x^4=(115+236i)(-5+4i)$

$=-575+460i-1180i+944i^2$

$x^4=-1519-720i$

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

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

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

$=-160$