TS EAMCET · Maths · Complex Number
\((\sqrt{3}+i)^7+(\sqrt{3}-i)^7\) is equal to
- A \(128 \sqrt{3}\)
- B \(256 \sqrt{3}\)
- C \(-128 \sqrt{3}\)
- D \(-256 \sqrt{3}\)
Answer & Solution
Correct Answer
(C) \(-128 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
\((\sqrt{3}+i)^7+(\sqrt{3}-i)^7\) Let \(\quad \sqrt{3}+i=z\) \(z=(\sqrt{3}+i)=r(\cos \theta+i \sin \theta)\) Then, \(\quad r \cos \theta=\sqrt{3}\) \(\ldots\) (i) \(r \sin \theta=1\) \(\ldots\) (ii) Eq. (i) + Eq. (ii), we get \(r^2\left(\sin ^2 \theta+\cos ^2 \theta\right)=3+1\)…
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