Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( i^{342} = -1 \)
Solution
Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.
Unlock Reviewed and approved by the UpStudy tutoring team
Like
Bonus Knowledge
To simplify \( i^{342} \), we can use the fact that the powers of \( i \) (the imaginary unit) cycle every four numbers: - \( i^1 = i \) - \( i^2 = -1 \) - \( i^3 = -i \) - \( i^4 = 1 \) To find \( i^{342} \), we first find the remainder of \( 342 \) when divided by \( 4 \): \( 342 \div 4 = 85 \) with a remainder of \( 2 \). So, \( 342 \mod 4 = 2 \). Therefore, \( i^{342} = i^2 = -1 \). Final answer: \(-1\)
