To find the value of \( i^{26} \), we can use the property of powers of \( i \) (the imaginary unit). The powers of \( i \) cycle every 4:
\[ \begin{align*} i^1 & = i \ i^2 & = -1 \ i^3 & = -i \ i^4 & = 1 \ \end{align*} \]
After \( i^4 \), the pattern repeats: \( i^5 = i \), \( i^6 = -1 \), \( i^7 = -i \), and so on.
To simplify \( i^{26} \), we can find the remainder when 26 is divided by 4:
\[ 26 \div 4 = 6 \quad \text{(remainder 2)} \]
This means:
\[ 26 = 4 \times 6 + 2 \]
Thus, \( i^{26} \) corresponds to \( i^2 \):
\[ i^{26} = i^2 = -1 \]
Therefore, the value equivalent to the complex number \( i^{26} \) is:
\[ \boxed{-1} \]
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