Question

Which of the following is equivalent to the expression ¡⁴¹?

A. 1
B. i
C. -i
D. -1

Answer 1

The expression ¡⁴¹ represents an imaginary unit raised to the power of 41.

The imaginary unit (i) is defined as the square root of -1.

When the imaginary unit is raised to any power, it follows a pattern of repetition every four powers: i, -1, -i, 1.

Since 41 is a multiple of 4 (41 ÷ 4 = 10 remainder 1), we can determine the equivalent expression by finding the remainder when dividing the exponent by 4.

In this case, the remainder is 1, so the equivalent expression is the first term in the pattern, which is i.

Therefore, the correct answer is B. i.