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Complex and Imaginary Numbers

Algebra IISophomoreUpdated October 25, 2026

Operations and rules for working with imaginary and complex numbers.

Complex and Imaginary Numbers

Negative inside radical: take i out of the radical (e.g., sqrt(-25) = 5i).

Powers of i: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1. Divide exponent by 4 to find remainder.

Imaginary number in denominator: multiply numerator and denominator by the complex conjugate of the denominator.

Absolute Value with i: for |a + bi|, evaluate sqrt(a^2 + b^2). Always simplify radicals first.

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