Re: Complex Number tutorial

On Jan 22, 6:00 pm, Rick Lyons <R.Lyons@xxxxxxxxxxxxxxx> wrote:
On Mon, 21 Jan 2008 18:56:34 -0800 (PST), buleg...@xxxxxxxxxxxxxxx
wrote:

  (snipped)



To understand rotational/sinusoidal solutions, however, we need to
understand complex numbers, which (perhaps) nobody really intuitively
understands.  I guess when it all boils down, the only way to get a
complete solution to a differential equation (one that includes not
just the correct frequeny, but the correct phasing), you need the
hidden magic of complex numbers going on "behind the scenes".

I know this sounds like rambling jibberish, and probably blows my
credibility, but, oh well.

Brent

Hi Brent,
    Don't worry.
Reaching some sort of comfortable understanding
of the true meaning (whatever that is) of complex numbers
is not at all easy.  I make no claim that I understand
their meaning.  I merely understand a little bit
about their behavior.

Remember, if complex numbers were easy to understand,
the great mathematician Karl Gauss would *NOT* have
called the j-operator "the shadow of shadows".

[-Rick-]

Thanks for your nice replies and encouragement. I read ( a lot of )
your book and Steve Smiths book. To some extent those two books
motivated me to do this stuff. Steve is a gifted writer and I feel
that you really struck a wonderful balance between hard math and
visual/descriptive content. In my opinion, you cannot just pick up
an Oppenheim/Shaeffer book and learn DSP. Way too hard. I've tried it
a couple of times over the years and can't get past about 20 pages -
too hard to see what is going on.

Brent
.

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