COMEDK · Maths · 3. Complex Number
Evaluate \(i^{2024}+i^{2025}+i^{2026}+i^{2027}\) (where \(i=\sqrt{-1})\)
- A 1
- B 0
- C -1
- D -i
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
\(\begin{array}{lr}\text { We have, } i^{2024}+i^{2025}+i^{2026}+i^{2027} & \\ =i^{4 \times(506)}+i^{4 \times 506+1}+i^{4 \times 506+2}+6^{4 \times 506+3} & {\left[\because i^{4 n}=1\right]} \\ =1+i+i^2+i^3 & {\left[\because i^2=-1\right]} \\ =1+i-1-i=0 & \end{array}\)
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 magnitude of the projection of the vector \(-\hat{\imath}+2 \hat{\jmath}-\hat{k}\) on the z -axis isCOMEDK 2025 Easy
- If \(f(x)=b e^{a x}+a e^{b x}\), then \(f^{\prime \prime}(0)=\)COMEDK 2019 Medium
- \(\int_{-\pi / 2}^{\pi / 2} \sin ^2 x d x\) is equal toCOMEDK 2023 Hard
- In the group \(\{1,2,3,4,5,6\}\) under multiplication \(\bmod 7,2^{-1} X_{7}^{4}=\)COMEDK 2018 Easy
- The solution of the differential equation \(\left(\frac{d y}{d x}\right) \tan y=\sin (x+y)+\sin (x-y)\) isCOMEDK 2023 Hard
- If the coefficients of \(x^2\) and \(x^3\) in the expansion of \((3 + kx)^9\) are equal, then the value of '\(k\)' isCOMEDK 2026 Easy
More PYQs from COMEDK
- A straight lines meets the coordinates axes at \(A\) and \(B\), so that the centroid of the \(\triangle O A B\) is \((1,2)\). Then, the equation of the line \(A B\) isCOMEDK 2015 Easy
- Which of the following is an intensive property?COMEDK 2020 Medium
- Two statements, one Assertion (A) and the other Reason (R) are given. Choose the correct option.
Assertion: Compound \([\mathrm{X}]\) reacts with Hydrazine in presence of \(\mathrm{KOH} /\) Glycol to form the product \([\mathrm{Y}]\).
COMEDK 2025 Medium - Identify the starting compound from the following data:
\(\mathrm{C}_6 \mathrm{H}_{14} \mathrm{O}(\mathrm{X})\) on reaction with \(\mathrm{HI}\) yields a haloalkane (A) and an alcohol (B). Compound (A) on reaction with aqueous \(\mathrm{NaOH}\) gives an alcohol (C). Compounds (B) and (C) on reaction with \(\mathrm{CrO}_3\) in anhydrous medium yields Butanone and Ethanal respectively.COMEDK 2023 Hard - Two similar coils \(A\) and \(B\) of radius '\(r\)' and number of turns '\(N\)' each are placed concentrically with their planes perpendicular to each other. If I and \(2 \mathrm{I}\) are the respective currents passing through the coils then the net magnetic induction at the centre of the coils will be:COMEDK 2024 Medium
- For one mole of \(\mathrm{NaCl}(s)\) the lattice enthalpy is
COMEDK 2015 Hard