AP EAMCET · Maths · Complex Number
\(\frac{(1+i)^{2011}}{(1-i)^{2009}}\) is equal to
- A -1
- B 1
- C 2
- D -2
Answer & Solution
Correct Answer
(D) -2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \frac{(1+i)^{2011}}{(1-i)^{2009}}=\frac{(\sqrt{2})^{2011}\left(\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}\right)^{2011}}{(\sqrt{2})^{2009}\left(\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}}\right)^{2009}} \\ & =\frac{(\sqrt{2})^2\left(e^{\frac{i…
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 \(\frac{x}{\cos \alpha}=\frac{y}{\cos \left(\frac{2 \pi}{3}-\alpha\right)}=\frac{z}{\cos \left(\frac{2 \pi}{3}+\alpha\right)}\), then the value of \((x+y+z)\) is equal toAP EAMCET 2020 Medium
- The points whose position vectors are \(2 \mathbf{i}+3 \mathbf{j}+4 \mathbf{k}, 3 \mathbf{i}+4 \mathbf{j}+2 \mathbf{k}\) and \(4 \mathbf{i}+2 \mathbf{j}+3 \mathbf{k}\) are the vertices ofAP EAMCET 2013 Easy
- The sum of squares of roots of the equation \(x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0\) isAP EAMCET 2022 Easy
- Let \(a, b\) and \(c\) be distinct and none of them is equal to 1 . If the lines \(x+a y+a=0\), \(b x+y+b=0\) and \(c x+c y+1=0\) are concurrent, then the value of \(\frac{a}{a-1}+\frac{b}{b-1}+\frac{c}{c-1}\) isAP EAMCET 2018 Medium
- If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-4 x+5=0\), then the quadratic equation whose roots are \(\alpha^2+\beta\) and \(\alpha+\beta^2\) isAP EAMCET 2018 Medium
- The constant ' \(\mathcal{C}\) ' of Lagrange's mean value theorem for the function \(f(x)=\frac{2 x+3}{4 x-1}\) defined on \([1,2]\) isAP EAMCET 2018 Easy
More PYQs from AP EAMCET
- Assertion (A) When an ideal gas is compressed adiabatically, its temperature and the average kinetic energy of the gas molecules increase.
Reason (R) The kinetic energy increases because of collisions of molecules with moving parts of wall only.AP EAMCET 2022 Easy - If \(m\) and \(\sigma^2\) are the mean and variance of the random variable \(X\), whose distribution is given by
ThenAP EAMCET 2009 Medium - A car moving at a speed \(v\) is stopped by a retarding force \(F\) in a distance \(s\). If the retarding force were \(3 F\), then the car will be stopped in a distanceAP EAMCET 2021 Easy
- The area of the triangle formed by the pair of lines \(23 x^2-\) \(48 x y+3 y^2=0\) with the line \(2 x+3 y+5=0\) isAP EAMCET 2024 Medium
- The points \(\mathrm{A}(-1,2,3), \mathrm{B}(2,-3,1), \mathrm{C}(3,1,-2)\)AP EAMCET 2025 Medium
- Let \(A_1\) be the area of the given ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\). Let \(A_2\) be the area of the region bounded by the curve which is the locus of mid point of the line segment joining the focus of the ellipse and a point \(P\) on the given ellipse, then \(A_1: A_2\) \(=\)AP EAMCET 2025 Hard