HP 15c - Manual (Page 76)

76 Section 3: Calculating in Complex Mode
76
Keystrokes Display
' 054- 12 Calculates e
iz
.
® 055- 34
÷ 056- 10 Calculates f(z).
|n 057- 43 32
Approximate the complex integral by integrating the function from 1 + 0i to 1 + 6i using a
i2 display format to obtain three significant digits. (The integral beyond 1 + 6i doesn't
affect the first three digits.)
Keystrokes Display
|¥
Run mode.
´i2
Specifies i2 format.
1
v 1.00 00 Enters first limit of integration,
1 + 0i.
1 v6 6
´V 1.00 00 Enters second limit of
integration, 1 + 6i.
´A -3.24 -01 Calculates I and displays Re(I)
= I
1
.
´% (hold) 3.82 -01 Displays Im(I) = I
2
.
® 7.87 -04 Displays Re(ΔI) = ΔI
1
.
´% (hold) 1.23 -03 Displays Im(ΔI) = ΔI
2
.
´•4 0.0008
This result I is calculated much more quickly than if I
1
and I
2
were calculated directly along
the real axis. .
Complex Potentials
Conformal mapping is useful in applications associated with a complex potential function.
The discussion that follows deals with the problem of fluid flow, although problems in
electrostatics and heat flow are analogous.
Consider the potential function P(z). The equation Im(P(z)) = c defines a family of curves
that are called streamlines of the flow. That is, for any value of c, all values of z that satisfy
the equation lie on a streamline corresponding to that value of c. To calculate some points z
k
on the streamline, specify some values for x
k
and then use _ to find the corresponding
values of y
k
using the equation
Im(P(x
k
+ iy
k
)) = c.
If the x
k
values are not too far apart, you can use y
k-1
as an initial estimate for y
k
. In this way,
you can work along the streamline and calculate the complex points z
k
= x
k
+ iy
k
. Using a
similar procedure, you can define the equipotential lines, which are given by Re(P(z)) = c.