=,
*
i*
=

=

Let *x*
= 1

arctg(1)
=
= =

= =
=
=
0

But
arctg(1)
=

**An
explanation of the paradox:**

The complex
logarithm is a multi-valued function.

Ln(*z*)
= ln|*z*|
+ *i*(arg
* z*
+ 2k),
* k*
= 0, ±1, ±2, ...

Ln(1)
= ln|1| + *i*(arg
(1) + 2k),
* k*
= 0, ±1, ±2, ...

If
we consider a branch Ln(1),
where
*k*
= 1 then

Ln(1) =
and the paradox disappears.

arctg(1)
= =
=

arctg(1)
=

by
Tetyana Butler