Q.

If x=−5+4i then x4+9x3+35x2−x+4=

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a

170

b

160

c

−170

d

−160

answer is D.

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Detailed Solution

x=−5+4i ⇒(x+5)2=−16 ⇒x2+10x=−41 ⇒x2+10x+41=0 x4+9x3+35x2−x+4 =x2(x2+10x+41) −x(x2+10x+41) +4(x2+10x+41)−160 =x2(0)−x(0)+x(0)−160 =−160
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