Q99 / 180 · COMEDK 2024 (Memory Based) · Mathematics

Evaluate $i^{2024}+i^{2025}+i^{2026}+i^{2027}$ (where $i=\sqrt{-1})$

  • A
    1
  • Correct answer
    B
    0
  • C
    -1
  • D
    -i

Solution

$\begin{array}{lr}\text { We have, } i^{2024}+i^{2025}+i^{2026}+i^{2027} & \\ =i^{4 \times(506)}+i^{4 \times 506+1}+i^{4 \times 506+2}+6^{4 \times 506+3} & {\left[\because i^{4 n}=1\right]} \\ =1+i+i^2+i^3 & {\left[\because i^2=-1\right]} \\ =1+i-1-i=0 & \end{array}$

Hence, the correct answer is option: 'B'.

Relevant Questions