"What is i to the 26th power?"
Mathematics · Middle School · Thu Feb 04 2021
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To find \( i \) to the 26th power, we need to remember that \( i \) is the imaginary unit, which is defined as \( \sqrt{-1} \). The powers of \( i \) follow a pattern:
- \( i^1 = i \) - \( i^2 = -1 \) - \( i^3 = -i \) - \( i^4 = 1 \)
You might notice that every four powers, the cycle repeats. So for \( i^{26} \), we can find the remainder when 26 is divided by 4 to determine where we are in the cycle.
\[ 26 \div 4 = 6 \text{ with a remainder of } 2 \]
This means that \( i^{26} \) is the same as \( i^2 \) because the remainder is 2. So:
\[ i^{26} = i^2 = -1 \]
Therefore, \( i \) to the 26th power is \( -1 \).