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An imaginary number is a mathematical concept that is used to extend the real number system. It is defined as a number that can be expressed as a real number multiplied by the imaginary unit \(i\), where: \[ i = \sqrt{-1} \] This means that \(i^2 = -1\). Imaginary numbers are typically expressed in the form \(bi\), where \(b\) is a real number.