WOLFRAM|DEMONSTRATIONS PROJECT

Tetraviews of Elementary Functions

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function
Sin
Cos
Exp
SubscriptBox[\(φ\), \(x, y\)]​
SubscriptBox[\(φ\), \(x, u\)]​
SubscriptBox[\(φ\), \(x, v\)]​
SubscriptBox[\(φ\), \(y, u\)]​
SubscriptBox[\(φ\), \(y, v\)]​
SubscriptBox[\(φ\), \(u, v\)]​
The natural living space of a function
zf(z)
with
z
being a complex variable is the two-dimensional complex space with coordinates
{z,f(z)}
or the four-dimensional real space with coordinates
{x=Re(z),y=Im(z),u=Re(f(z)),v=Im(f(z))}
. This Demonstration shows three-dimensional projections from the four-dimensional space. By carrying out rotations in the four-dimensional space, different views of the function
f(z)
can be obtained (including views of the inverse function
-1
f
(z)
).