Re: TI-85 and log(-4)
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Re: TI-85 and log(-4)
On Fri, 25 Jul 1997, jesse samuels wrote:
> anybody know where euler got his formula, and what use it has? I
> vaguely remember using it in diff e q, but I can't remember why...
I'd say it comes from the definition of complex exponential function
e^z = e^x * (cos y + i*sin y)
which is motivated by requirements that make e^z a natural extension of
the real exponential function e^x (won't list them here).
For z = i*y we get from the definition of e^z the Euler formula
e^(i*y) = cos y + i*sin y
I'm not much of a mathematian myself, but if you want to study your Euler
well, there are more than seventy (70) volumes of his Collected Works
available!
The formula is extremely handy, for instance, where (complex) trigonometry
is used a lot, as you can tell by the sin and cos functions above.
Jani
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