• # question_answer If $x=3+i$,  then ${{x}^{3}}-3{{x}^{2}}-8x+15=$ [UPSEAT 2003] A) 6 B) 10 C) - 18 D) - 15

$x=3+i\,\Rightarrow \,\,x-3=i\,$ $\Rightarrow$  $\,{{x}^{2}}-6x+10=0$  Þ  ${{x}^{3}}-3{{x}^{2}}-8x+15$  $=x({{x}^{2}}-6x+10)+3\,({{x}^{2}}-6x+10)-15$ $=x(0)+3(0)-15=-15$.