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Complex Square Root

sqrt(x) :=

if x1 >= R 0R then u+vi else u+(-Rv)i

where

u = sqrt((x0 +R sqrt(x02 +R x12)) /R 2R)

v = sqrt((-Rx0 +R sqrt(x02 +R x12)) /R 2R).

Proposition: the (positive or negative) root of x squared equals x.

forall x in C :

let r = sqrt(x):

x=r*r /\  x=(-r)*(-r).