Lambert W Function (hp-42s)

[Juan14]

I don't own a hp-42s, line 21 should be 1E-10 or something like that in the hp-42s. My program can take advantage of the fact that the hp-42s can handle complex numbers. For example let's consider a infinite tower of the imaginary number i, i^i^i^i......
We have i^i^i^i...... = x; i^(i^i^i^i)...... = x; i^x = x or i = x^(1/x) taking ln on both sides of the equation
ln(i) = 1/x ln(x); -ln(i) = -1/x ln(x); -ln(i) = 1/x ln(1/x), calling W to the Lambert W function.
W(-ln(i)) = W(1/x ln(1/x)); W(-ln(i)) = ln(1/x); 1/x = exp(W(-ln(i))) and finally x=exp(-W(-ln(i))).
In the calculator:
0 [ENTER] 1 [COMPLEX] [LN] [+/-] [XEQ] LWF [+/-][■][E↑X]
You get 4.3828293673E-1 i 3.605924718714E-1
so i^i^i^i...... ≈ 0.43828293673+ i 0.3605924718714