25. \( i^{12} \)

To determine \( i^{12} \), we first need to understand that \( i \) is the imaginary unit, defined as \( i = \sqrt{-1} \). The powers of \( i \) cycle through four values: \( i^1 = i \), \( i^2 = -1 \), \( i^3 = -i \), and \( i^4 = 1 \). After reaching \( i^4 \), the pattern repeats: \( i^5 = i \), \( i^6 = -1 \), and so on. Since \( 12 \mod 4 = 0 \), we find that \( i^{12} \) corresponds to \( i^0 = 1 \). In conclusion, \( i^{12} = 1 \).