       Re:graphing x^2 + 4 on x, y, nad i

• To: mathgroup at smc.vnet.net
• Subject: [mg61862] Re:[mg61238]graphing x^2 + 4 on x, y, nad i
• From: "G. Raymond Brown" <gbrown at runbox.com>
• Date: Wed, 2 Nov 2005 04:09:30 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Scott,

Thanks.  This provides an illuminating depiction of complex functions at
both zeros and poles.

-GRB-

Scott Hemphill <hemphill at hemphills.net>wrote:

thomas <likothecat at hotmail.com> writes:

> Hi,
>
> Is it possible to make a 3d type of graph using the x, y, and i axes
> for the equation y = x ^ 2 + 4?

I use something like:

Plot4D[f_, {x_, xmin_, xmax_}, {y_, ymin_, ymax_}, opts___] :=
Plot3D[{Abs[f], Hue[Arg[f]/(2*Pi)]}, {x, xmin, xmax}, {y, ymin, ymax},
opts]

This function plots the absolute value of the complex function as the height,
and the argument as the hue.

Then:

z = (x+I*y)

Plot4D[z^2+4,{x,-5,5},{y,-5,5}]

The zeros can be identified by the kinks in the surface, and they are also
identified as the places which are surrounded by all the hue colors.

Scott
G. Raymond Brown, Ph.D.
Scientific Program Coordinator
Division of Science and Mathematics
Morehouse College

```

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