Simplify each power of i. 1/i^-11

Key Concepts

Imaginary Unit (i)

The imaginary unit 'i' is defined as the square root of -1. It is a fundamental concept in complex numbers, allowing for the extension of the real number system to include solutions to equations that do not have real solutions, such as x^2 + 1 = 0. Powers of 'i' cycle through four values: i^0 = 1, i^1 = i, i^2 = -1, and i^3 = -i.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For example, a^-n = 1/a^n. This concept is crucial for simplifying expressions involving negative powers, as it allows us to rewrite them in a more manageable form, often leading to easier calculations.

Simplifying Complex Expressions

Simplifying complex expressions involves reducing them to their simplest form, often by applying properties of exponents and the rules of arithmetic. In the case of powers of 'i', this means using the cyclical nature of 'i' and the rules for negative exponents to rewrite the expression in a more straightforward manner, facilitating easier computation and understanding.