previous up next
Go backward to Fundamental Theorem of Algebra
Go up to Top
Go forward to Complex Conjugate
RISC-Linz logo

Complex Square Root

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

Author: Wolfgang Schreiner
Last Modification: November 16, 1999

previous up next