  Let varphi_n:C^n times C^n->C,
varphi_n((x_1,...,x_n),(y_1,...,y_n))=sum_{i=1}^n (x_i-y_i)^2. We say that
f:C^n->C^n preserves distance d>=0, if for each X,Y in C^n varphi_n(X,Y)=d^2
implies varphi_n(f(X),f(Y))=d^2. We prove: if n>=2 and a continuous f:C^n->C^n
preserves unit distance, then f has a form I circ (rho,...,rho), where
I:C^n->C^n is an affine mapping with orthogonal linear part and rho:C->C is the
identity or the complex conjugation. For n >=3 and bijective f the theorem
follows from Theorem 2 in [8].
