COMEDK · Maths · 3. Complex Number
\(\text { The value of } \dfrac{i^{1004}+i^{1006}+i^{1008}+i^{1010}+i^{1012}}{i^{510}+i^{508}+i^{506}+i^{504}+i^{502}} \text { is }\)
- A 1
- B \(-\)i
- C i
- D \(-1\)
Answer & Solution
Correct Answer
(D) \(-1\)
Step-by-step Solution
Detailed explanation
The powers of \(i\) repeat in a cycle of \(4\): \(i^{1} = i\), \(i^{2} = -1\), \(i^{3} = -i\), \(i^{4} = 1\). For the numerator, we have \(i^{1004} + i^{1006} + i^{1008} + i^{1010} + i^{1012}\). Since \(1004, 1008, 1012\) are multiples of \(4\),…
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 maximum area of a rectangle that can be inscribed in a circle of radius 2 units is (in square units)COMEDK 2019 Medium
- What will be the equation of the circle whose centre is \((1,2)\) and which passes through the point \((4,6)\) ?COMEDK 2021 Medium
- If \(A+B+C=180^{\circ}\), then \(\Sigma \tan \frac{A}{2} \tan \frac{B}{2}\) is equal toCOMEDK 2013 Easy
- The argument of the complex number \(\sin \left(\frac{6 \pi}{5}\right)+i\left(1+\cos \frac{6 \pi}{5}\right)\) isCOMEDK 2018 Medium
- Which one of the following is not true always?COMEDK 2016 Easy
- If \(\omega=\frac{-1+\sqrt{3 i}}{2} \operatorname{then}\left(3+\omega+3 \omega^{2}\right)^{4}\) isCOMEDK 2013 Easy
More PYQs from COMEDK
- The expression \(\frac{\sin \theta-2 \sin ^3 \theta}{2 \cos ^3 \theta-\cos \theta}\) is equal toCOMEDK 2024 Medium
- A gas bubble of volume \(2 \mathrm{~cm}^3\) rises from the bottom of a pond of depth 10 m at \(17^0 \mathrm{C}\). What will be the volume of the bubble when it reaches the surface of the pond? Atmospheric temperature is \(27^{\circ} \mathrm{C}\) and the pressure at the bottom of the pond is double that of the pressure at the surface.COMEDK 2025 Medium
- When a charged particle moves perpendicular to a uniform magnetic field, thenCOMEDK 2016 Easy
- A copper and a steel wire of same diameter are connected end to end. A deforming force \(F_1\) is applied to the wire which causes an elongation of \(1 \mathrm{~cm}\). The two wires will haveCOMEDK 2022 Easy
- The equation \(\frac{x^{2}}{2-\lambda}-\frac{y^{2}}{\lambda-5}-1=0\) represents an ellipse ifCOMEDK 2019 Easy
- A point marked on a ring of radius 2 cm is in contact with a horizontal plane. Now the ring is rolled forward half a revolution along the positive X - direction. Then the angle made by the displacement vector of the point with the X - axis is:COMEDK 2025 Medium