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The question asks for the value of \( i^{146} \), where \( i \) is the imaginary unit, defined as \( i = \sqrt{-1} \).

To solve this, we use the cyclical property of powers of \( i \):
\[
i^1 = i, \quad i^2 = -1, \quad i^3 = -i, \quad i^4 = 1, \quad \text{and then it repeats every 4 powers.}
\]

To find \( i^{146} \), we calculate the remainder of 146 when divided by 4:
\[
146 \div 4 = 36 \text{ remainder } 2
\]
Thus, \( i^{146} = i^2 \).

From the cyclical pattern, we know:
\[
i^2 = -1
\]

Therefore, the value of \( i^{146} \) is \( \boxed{-1} \), which corresponds to option (B).

Do you want more details or have any questions? Here are five related questions to deepen your understanding:

1. How do powers of \( i \) form a cycle?
2. What is the value of \( i^{202} \)?
3. How is the remainder important when dealing with powers of \( i \)?
4. Can you explain the properties of imaginary numbers?
5. How do complex numbers apply to real-world problems?

**Tip:** For higher powers of \( i \), always reduce the exponent modulo 4 to use the repeating pattern.

Learn how to find the value of i^146 by utilizing the cyclical properties of powers of the imaginary unit i. This example demonstrates the application of modulo operations and pattern recognition, suitable for students in Grades 9-12.

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