TS EAMCET · Maths · Complex Number
A value of \(n\) such that \(\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1\) is
- A \(12\)
- B \(3\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(12\)
Step-by-step Solution
Detailed explanation
Given, \(\begin{aligned} & \left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1 \\ & \left(\operatorname{cis} \frac{\pi}{6}\right)^n=1\end{aligned}\) \(\therefore\) Only \(n=12\) satisfies this equation.
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
- Let x be a real number. Match the following:
TS EAMCET 2022 Easy - In a \(\triangle A B C, \cot A+\cot B+\cot C=\)TS EAMCET 2020 Hard
- TS EAMCET 2018 Medium
- Let \(\lim _{t \rightarrow 0}(1+5 t)^{\frac{1}{t}}=K\) and \(X\) be the random variable representing number of successes in 100 independent trials. If the probability of success in each trial is 0.05 , then the probability of getting at least one success isTS EAMCET 2019 Easy
- If cis \(\alpha\) is the common value of \((-1)^{1 / 4}\) and \((-i)^{1 / 2}\) then \(\tan \alpha=\)TS EAMCET 2022 Hard
- If \(\vec{a}, \vec{b}\) are two vectors such that \(|\vec{a}|=3,|\vec{b}|=4,|\vec{a}+\vec{b}|=\sqrt{37},|\vec{a}-\vec{b}|=k\) and \((\vec{a}, \vec{b})=\theta\), then \(\frac{4}{13}(k \sin \theta)^2=\)TS EAMCET 2024 Medium
More PYQs from TS EAMCET
- Consider a system of blocks \(X, A\) and \(B\) as shown in the figure. The blocks \(A\) and \(B\) have equal mass and are connected by a massless string through a massless pulley. The coefficient of friction between block \(A\) and \(X\) or \(B\) and \(X\) is 0.5 . If block \(X\) moves on the horizontal frictionless surface what should be Its minimum acceleration such that blocks \(A\) and \(B\) remain stationary. \((g=\) acceleration due to gravity.)
TS EAMCET 2019 Hard - The order of covalent character of KF, KI, \(\mathrm{KCl}\) isTS EAMCET 2016 Medium
- Let be a line passing through and is a line perpendicular to and passing through The area of the triangle formed by and -axis isTS EAMCET 2021 Easy
- Two logic gates are connected as shown in the figure. If the inputs are \(A=1\) and \(B=0\), then the values of \(y_1\) and \(y_2\) respectively are
TS EAMCET 2024 Easy - A codon has a sequence of \(\underline{A}\), and specifies a particular \(\underline{B}\) that is to be incorporated into a \(\underline{C}\). What are \(\underline{A}, \underline{B}, \underline{C}\) ? \(\underline{A} \quad \underline{B} \quad \underline{C}\)TS EAMCET 2009 Medium
- Two uniform strings \(A\) and \(B\) made of steel are made to vibrate under the same tension. If the first overtone of \(A\) is equal to the second overtone of \(B\) and if the radius of \(A\) is twice that of \(B\), the ratio of the lengths of the strings is :TS EAMCET 2003 Medium