AP 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
- The points \((2,3,5),(-1,5,-1)\) and \((4,-3,2)\) formAP EAMCET 2017 Easy
- If the tangent drawn to the parabola \(y^2=4 x\) at \(\left(t^2, 2 t\right)\) is the normal to the ellipse \(4 x^2+5 y^2=20\) at \((\sqrt{5} \cos \theta, 2 \sin \theta)\), thenAP EAMCET 2019 Medium
- If , thenAP EAMCET 2021 Hard
- Let \(A B C\) be a triangle. Let \(u=\mathbf{A B}\) and \(v=\mathbf{A C}\). If \(D\) is a middle point of \(B C\), then \(\mathbf{A D}=\)AP EAMCET 2020 Easy
- The lines \(L_1: y-x=0\) and \(L_2: 2 x+y=0\) intersect the line \(L_3: y+2=0\) at \(P\) and \(Q\) respectively. The bisector of the acute angle between \(\mathrm{L}_1\) and \(\mathrm{L}_2\) intersects \(\mathrm{L}_3\) at \(\mathrm{R}\).
Statement 1: PR : RQ \(=2 \sqrt{2}: \sqrt{5}\)
Statement 2: In any triangle, the bisector of an angle divides the triangle into two similar triangles.AP EAMCET 2023 Medium - The equation of tangent to the curve \(y=5 x^2-3 x+7\) at the point \((-1,4)\) is ......AP EAMCET 2020 Easy
More PYQs from AP EAMCET
- If \(\cos \theta=\frac{-3}{5}\) and \(\theta\) does not lie in second quadrant, then \(\tan \frac{\theta}{2}=\)AP EAMCET 2025 Medium
- If the roots of the equation \(x^3+3 p x^2+3 q x-8=0\) are in an arithmetic progression then \(2 p^3-3 p q=\)AP EAMCET 2017 Medium
- If the equation having the roots as the values obtained oy diminishing each root of the equation \(x^3-3 x^2+2 x-1=0\) by \(\mathrm{K}\) is \(\mathrm{x}^3-\mathrm{x}-1=0\), then \(\mathrm{K}=\)AP EAMCET 2023 Easy
- If \(x^2+y^2+6 x+2 k y+25=0\) to touch \(Y\)-axis, then \(k=\)AP EAMCET 2020 Easy
- If \(p\) th, \(q\) th, \(r\) th terms of a geometric progression are the positive numbers \(a, b\) and \(c\) respectively, then the angle between the vectors \(\left(\log a^2\right) \mathbf{i}+\left(\log b^2\right) \mathbf{j}+\left(\log c^2\right) \mathbf{k} \quad\) and \((q-r) \mathbf{i}+(r-p) \mathbf{j}+(p-q) \mathbf{k}\) isAP EAMCET 2012 Hard
- The logic gate equivalent to the combination of logic gates shown in the figure is
AP EAMCET 2025 Medium