TS EAMCET · Maths · Complex Number
If \(\mathrm{i}^2=-1\) then \((1+\sqrt{3} \mathrm{i})^{2022}-(\sqrt{3}-\mathrm{i})^{2022}=\)
- A \(2^{2023}\)
- B 0
- C \(2^{2022}\)
- D \(3^{1011}\)
Answer & Solution
Correct Answer
(A) \(2^{2023}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text (1+\sqrt{3} i)^{2022}-(\sqrt{3}-i)^{2022} \\ & =2^{2022}\left(\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)^{2022}-2^{2022}\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^{2022} \\ & =2^{2022}\left[\left(\cos \frac{\pi}{3}+i \sin…
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 area (in square units) of the region enclosed by the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) isTS EAMCET 2010 Hard
- If \(\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi\), thenTS EAMCET 2019 Easy
- If \(y=2 x\) is a tangent to the curve \(y^2=a x^3+b\) at \((1,2)\), then \((a, b)=\)TS EAMCET 2018 Medium
- If and are the roots of the quadratic equation thenTS EAMCET 2019 Easy
- The angle between the line joining the points \((1,-2),(3,2)\) and the line \(x+2 y-7=0\) isTS EAMCET 2007 Easy
- The area (in sq. units) of the quadrilateral formed by the tangents drawn at the end points of the latus rectum to the ellipse \(S \equiv \frac{x^2}{16}+\frac{y^2}{12}=1\) isTS EAMCET 2020 Easy
More PYQs from TS EAMCET
- is a rectangular loop made of uniform wire. If what is the magnetic force per unit length acting on wire due to wire if ammeter reads (The length of and are large in comparison with other two sides)
TS EAMCET 2021 Easy - A tangent is drawn at \((\beta \sqrt{3} \cos \theta, \sin \theta)\) \(\left(0 < \theta < \frac{\pi}{2}\right)\) to the ellipse \(\frac{x^2}{27}+\frac{y^2}{1}=1\). The value of \(\theta\) for which the sum of the intercepts on the coordinate axes made by this tangent attains the minimum, isTS EAMCET 2019 Easy
- 5 persons entered a lift cabin in the cellar of a 7 -floor building apart from cellar. If each of them independently and with equal probability can leave the cabin at any floor out of the 7 floors beginning with the first, then the probability of all the 5 persons leaving the cabii at different floors isTS EAMCET 2023 Hard
- If \(\mathbf{a}=2 \hat{\mathbf{j}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{c}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) are three vectors, then \(|(\mathbf{a} \times \mathbf{b}) \times \mathbf{c}|=\)TS EAMCET 2019 Easy
- A solid has a structure in which 'W' atoms are located at the corners of a cubic lattice, oxygen atoms at the edge centre and \(\mathrm{Na}\) atom at the body centre. The formula of the compound isTS EAMCET 2022 Medium
- A simple pendulwm of length \(L\) carries a bob of mass \(m\). When the bob is at its lowest position, it is given that the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal, the net force on the bob isTS EAMCET 2016 Hard