AP 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 \(r^2\left(\sin ^2 \theta+\cos ^2 \theta\right)=3+1\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Solve \(\tan (x)+\sec (x)=\sqrt{3}, x \in[0,2 \pi]\)AP EAMCET 2020 Medium
- The transformed equation of \(x^2-y^2+2 x+4 y=0\) when the origin is shifted to the point \((-1,2)\) isAP EAMCET 2024 Easy
- If \(\frac{1}{2} \operatorname{Sin}^{-1}\left(\frac{3 \sin 2 \theta}{5+4 \cos 2 \theta}\right)=\operatorname{Tan}^{-1} x\) then \(x=\)AP EAMCET 2025 Medium
- The value of the expression
\(\begin{aligned}
& \frac{1+\sin 2 \alpha}{\cos (2 \alpha-2 \pi) \tan \left(\alpha-\frac{3 \pi}{4}\right)} \\
& -\frac{1}{4} \sin 2 \alpha\left[\cot \frac{\alpha}{2}+\cot \left(\frac{3 \pi}{2}+\frac{\alpha}{2}\right)\right]
\end{aligned}\)AP EAMCET 2016 Medium - The equation of the tangent to the curve \(y=x^3-2 x+7\) at the point \((1,6)\) isAP EAMCET 2024 Easy
- A point \(C\) with position vector \(\frac{3 \bar{a}+4 \bar{b}-5 \bar{c}}{3}\) (where \(\bar{a}, \bar{b}\) and \(\bar{c}\) are non coplanar vectors) divides the line joining \(A\) and \(B\) in the ratio \(2: 1\). If the position vector of \(A\) is \(\bar{a}-2 \bar{b}+3 \bar{c}\), then the position vector of \(B\) isAP EAMCET 2017 Easy
More PYQs from AP EAMCET
- If a point \(\mathrm{C}\) divides the line segment joining the points with the position vectors \(2 \hat{i}-3 \hat{j}+2 \hat{k}\) and \(3 \hat{i}-\hat{j}-2 \hat{k}\) in the ratio \(2: 3\), then the distance of \(\mathrm{C}\) from the point with position vector \(2 \hat{i}-\hat{j}+\hat{k}\) isAP EAMCET 2023 Easy
- If one of the lines given by the pair of lines \(3 x^2-2 y^2+a x y=0\) is making an angle \(60^{\circ}\) with x -axis then \(\mathrm{a}=\)AP EAMCET 2025 Medium
- If \(\mathbf{a} \cdot \hat{\mathbf{i}}=\mathbf{a} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}})=\mathbf{a} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\), then \(\mathbf{a}\) is equal toAP EAMCET 2002 Easy
- A system is taken from state to state along two different paths. The heat absorbed and work done by the system along these two paths are and respectively, thenAP EAMCET 2021 Medium
- If the straight lines \(2 x-y+1=0\), \(4 x+y+2=0\) and \(x+y-k=0\) are concurrent, then \(k\) equalsAP EAMCET 2021 Easy
- The coefficient of friction between object and substance, if we need to move an object of weight \(150 \mathrm{~N}\) on a horizontal surface with a force of \(75 \mathrm{~N}\), isAP EAMCET 2022 Medium