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Absolute Square
Plot
Alternate form
abs(x)^2
Alternate form assuming x is real
x^2
Root
x = 0
Derivative
d/dx(x x^*) = x^* + x (assuming a function from reals to reals)
Indefinite integral assuming all variables are real
integral x x^* dx = x^3/3 + constant
Global minimum
min{x x^*} = 0 at x = 0
Alternative representation
x x^* = (x abs(x)^2)/x
x x^* = x (-x + 2 Re(x))
x x^* = x (x - 2 i Im(x))