MHT CET · Maths · Complex Number
If \(x=1+2 i\), then the value of \(x^3+7 x^2-x+16\) is
- A -17 -24 i
- B -17 + 24 i
- C 17 - 24 i
- D 17 + 24 i
Answer & Solution
Correct Answer
(B) -17 + 24 i
Step-by-step Solution
Detailed explanation
We have \(x-1=2 i \quad \Rightarrow x^2-2 x+5=0\)
\(x^3+7 x^2-x+16 =x\left(x^2+7 x-1\right)+16 \)
\(=x[(0)+9 x-6]+16 \)
\(=9 x^2-6 x+16 \)
\(=9\left(x^2-2 x+5\right)+12 x-29 \)
\(=-17+24 i\)
\(x^3+7 x^2-x+16 =x\left(x^2+7 x-1\right)+16 \)
\(=x[(0)+9 x-6]+16 \)
\(=9 x^2-6 x+16 \)
\(=9\left(x^2-2 x+5\right)+12 x-29 \)
\(=-17+24 i\)
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