AP EAMCET · Maths · Complex Number
If \(x=-5+2 \sqrt{-4}\), then the value of \(x^4+9 x^3+35 x^2-x+4\) is
- A \(80\)
- B \(160\)
- C \(-160\)
- D \(-80\)
Answer & Solution
Correct Answer
(C) \(-160\)
Step-by-step Solution
Detailed explanation
\(x=-5+2 \sqrt{-4}\) \(\begin{aligned} & x+5=4 i \\ & (x+5)^2=(4 i)^2 \\ & x^2+10 x+25=-16 \\ & x^2+10 x+41=0\end{aligned}\) Let \(x^4+9 x^3+35 x^2-x+4=\left(x^2+10 x+41\right)(p(x))+\mathrm{R}\)…
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