sqrt(1+i)

[roadrunner]

I created a little program to return the exact result for nested square roots of a complex number:

Code:


#pragma mode( separator(.,;) integer(h32) )

rootroot(a,n);

#cas
rootroot(a,n):=
BEGIN
 local x,y,ra,ia;
 ra:=RE(a);
 ia:=IM(a); 
 y=√(-ra+√(ra^2+ia^2))/√2;
 x=ia/(2*y);
 if n==1 then return x+y*i; end;
 return rootroot(x+y*i,n-1);
END;
#end

It crashes the emulator for values of n 6 or greater. Example:

rootroot(1+i,5) works but rootroot(1+i,6) crashes.

However, approx(rootroot(1+i,6)) returns the correct approximate answer, which tells me the program is returning a correct answer but the display can't handle it, and sits there with an hour glass in the corner.

What am I doing wrong?

-road
-edited a grammatical error