A negative square cannot exist. Only existing in theory, it must be written positive and noted so by attaching its broken-down form with a symbol known as i. Let's assume that i is not a variable, but a number modifier that works in a series. i on its own does nothing but exist in the quation. However, i² equates to -1, which will affect the number
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It also helps see they're usefulness when you know Euler's identity: e^(i*omega*t) = cos(omega*t) + i*sin(omega*t), so if omega is imaginary it would represent oscillation and if omega is real it would represent damping. Complex omegas would represent a combination of the two. That's boatloads useful when solving differential wave equations (Schroedinger's equation, Maxwell's equations in freespace, Kirchoff's rules applied to complex impedences, etc.)
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