ACOS logarithmic form

[Dieter]

(04-28-2016 05:03 PM)Claudio L. Wrote:  Before somebody jumps and says "it's the same!", let's try a couple of cases:
(...)
Very subtle...

I wouldn't call this subtle, but obvious. At least as long as you do not forget that a square root has both a positive and a negative value:

Code:

   Z:=2

   ±sqrt(2^2-1)
 = 1.73 or -1.73

   i · ±sqrt(1-2^2)
 = i · ±sqrt(-3) 
 = i · ±1.73i
 = -1.73 or 1.73

----------------------------

   Z:=2+3i

   ±sqrt(Z^2-1)
 = ±sqrt(-6+12i)
 = 1.92+3.11i or -1.92-3.11i

   i · ±sqrt(1-Z^2)
 = i · ±sqrt(6-12i)
 = i · ±(3.11-1.92i)
 = 1.92+3.11i or -1.92-3.11i

----------------------------

   Z:=2-3i

   ±sqrt(Z^2-1) 
 = ±sqrt(-6-12*i) 
 =  1.92-3.11i or -1.92+3.11i

   i · ±sqrt(1-Z^2)
 = i · ±sqrt(6+12*i)
 = i · ±(3.11+1.92i)
 = -1.92+3.11i or 1.92-3.11i

So it's actually OK to jump in and say "it's the same!". ;-)

Dieter