Calculator test

[Commie]

(12-08-2024 08:38 PM)carey Wrote:  There is a workaround for the TI-84 Plus inability to accept complex arguments for its trig functions and their inverses. Since the TI-84 Plus exponential function (e^) does accept complex arguments, sine and cosine can be defined in terms of e^ using Euler ‘s formulas:

\[\cos(z) = \frac{e^{iz} + e^{-iz}}{2}\]
\[\sin(z) = \frac{e^{iz} - e^{-iz}}{2i}\]


In Mode, set angle to radians and select complex polar. After calculation, select complex rectangular for conversion to rectangular form. The LHS (which can’t be input directly) can be obtained by working on the RHS.
\[ \sin(1+2i) = \frac{e^{i *(1 + 2i)} - e^{-i *(1 + 2i)}}{2i}\]
\[ \sin(1+2i) = 3.165778 + 1.959601i \]
It’s cumbersome, but works!

A similar workaround applies to the Casio 9860gii and CG50 calculators as they also have complex argument limitations for trig functions but not for e^.

Thanks Carey, I know about these equations and I know how to derive them from Eulers identity, however until today they mean a great deal more now, especially with your input to confirm.
Could I just ask, what overlay are you using, in your browser, which makes math easy to print/read?

Cheers
Darren