JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(a\) and \(b\) are real numbers such that \((2+\alpha)^{4}=a+b \alpha,\) where \(\alpha=\frac{-1+i \sqrt{3}}{2},\) then \(a+b\) is equal to
- A \(57\)
- B \(33\)
- C \(24\)
- D \(9\)
Answer & Solution
Correct Answer
(D) \(9\)
Step-by-step Solution
Detailed explanation
\(\alpha=\omega\) \(\Rightarrow \quad(2+\omega)^{4}= a + b \omega\) \(\Rightarrow \quad 2^{4}+4.2^{3} \omega+6.2^{2} \omega^{3}+4.2 \cdot \omega^{3}+\omega^{4}\) \(\Rightarrow \quad= a + b \omega\) \(\Rightarrow \quad 24+24 \omega^{2}+33 \omega= a + b \omega\)…
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