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Absolute Square

Plot

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 representations

x x^* = (x abs(x)^2)/x

x x^* = x (-x + 2 Re(x))

x x^* = x (x - 2 i Im(x))

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