AP EAMCET · Maths · Complex Number
If \(x^6=(\sqrt{3}-i)^5\), then the product of all of its roots is
- A \(2^5(\sqrt{3}+i)\)
- B \(\frac{2^6}{\sqrt{3}+\mathrm{i}}\)
- C \(2^6(\sqrt{3}-i)\)
- D \(\frac{2^6}{\sqrt{3}-\mathrm{i}}\)
Answer & Solution
Correct Answer
(D) \(\frac{2^6}{\sqrt{3}-\mathrm{i}}\)
Step-by-step Solution
Detailed explanation
NO SOLUTION
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
- If \(\sin (x+3 \alpha)+3 \sin (x-\alpha)=0\), thenAP EAMCET 2017 Easy
- In the interval \(\left(\frac{1}{\mathrm{e}}, \mathrm{e}\right)\), a decreasing function among the following functions isAP EAMCET 2023 Medium
- AP EAMCET 2020 Medium
- Let \(\vec{b}=3 \hat{i}-2 \hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}-\hat{j}-\hat{k}\) be two vectors. If \(\vec{a}\) is a vector such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then \(|\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}|=\)AP EAMCET 2023 Medium
- If \(A=\left[\begin{array}{cc}1 & -2 \\ 4 & 5\end{array}\right]\) and \(f(t)=t^2-3 t+7\), then \(f(A)+\left[\begin{array}{cc}3 & 6 \\ -12 & -9\end{array}\right]\) is equal toAP EAMCET 2008 Medium
- If the straight lines \(2 x+3 y-1=0\), \(x+2 y-1=0\) and \(a x+b y-1=0\) form a triangle with orthocentre at the origin, then \((a, b)=\)AP EAMCET 2018 Medium
More PYQs from AP EAMCET
- If \({ }^{(n-1)} C_r=\left(k^2-3\right){ }^n C_{r+1}\), then an interval containing the values of \(k\), isAP EAMCET 2017 Easy
- If \(A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right]\), then \(A A^T\) is aAP EAMCET 2022 Easy
- Identify the correct statement (s) from the following
a) Protective power of a lyophilic sol is more if its gold number is more
b) In the coagulation of negative sols, the coagulating power of cations follow the order \(\mathrm{Na}^{+}>\mathrm{Ba}^{2+}>\mathrm{Al}^{3+}\)
c) Cloud is a solid in gas type of colloid
d) Physical adsorption is non-specific and multilayered at high pressure.AP EAMCET 2017 Easy - Two bodies A and B of masses 2 m and m are projected vertically upwards from the ground with velocities \(u\) and 2 u respectively. The ratio of the kinetic energy of body A and the potential energy of body B at a height equal to half of the maximum height reached by body A isAP EAMCET 2024 Medium
- A current \(I=10 \mathrm{~A}\) is passed through the part of a circuit shown in the figure. What will be the potential difference between \(A\) and \(B\) when \(I\) is decreased at constant rate of \(10^2 \mathrm{As}^{-1}\) at the beginning ?
AP EAMCET 2020 Hard - Let \(\alpha, \beta\) be the roots of the equation \(x^2-|a| x-|b|=0\) such that \(|\alpha| < |\beta|\). If \(|a| < \beta-1\), then the positive root of \(\log _{\mid \text {여 }}\left(\frac{x^2}{\beta^2}\right)-1=0\), isAP EAMCET 2019 Medium