i

In mathematics, particularly in complex analysis, "i" represents the imaginary unit. It is defined as the square root of -1, meaning that \( i^2 = -1 \). This concept extends our number system beyond real numbers, allowing us to solve equations like \( x^2 + 1 = 0 \), which have no real solutions. Imaginary numbers, combined with real numbers, form complex numbers (e.g., 3 + 4i). These are crucial in advanced fields such as engineering, physics, and signal processing, helping analyze phenomena like wave behavior and electrical currents.