|Re: WP 34S : Operation with complex numbers|
Message #3 Posted by Jeff O. on 31 Aug 2011, 4:27 p.m.,
in response to message #1 by Miguel Toro
As Walter reports, you are entering it correctly. Prior to Walter's repsonse I prepared the following. Not sure if it is pertinent, but I will let it stand.
I note the following: if you take sin(1.5708+i1.5239) on all three calculators, you get 2.4040 (plus a small imaginary component that would be zero with infinite precision.) If you take sin(1.5708-i1.5239) on all three calculators, you get 2.4040. So apparently both answers are valid. Being mostly a math dummy, I googled “complex arcsin” (actually I use startpage, but “startpaged” is not a common term for “entered into an internet search engine”) and found the following at wolfram.com:
The inverse sine is a multivalued function and hence requires a branch cut in the complex plane… This follows from the definition of sin-1 z as:
sin-1 z = -i ln (-i z + (1 - z 2) 1/2)
If I use the above formula, and use the positive value of the square root, I get the answer that the 15C and 42s provide. If I use the negative value of the square root, I get the value that wp34s provides. I do not know if that is how wp34s (prior to the next revision if it is to be changed) calculates the inverse sine of a complex value.
edit: Per Pauli's correction, the above formula should be:
sin-1 z = -i ln (i z + (1 - z 2) 1/2)
I'll leave the mistake for posterity.
Edited: 31 Aug 2011, 9:10 p.m.