Find the streamlines of the flows associated with the complex function Z SOLUTION The streamlines corresponding to fi(z) = x - iy satisfy the system dx dy dt dt x -y und so x(t) = c₁e¹ and y(t) = c₂e¹¹. By multiplying these two parametric equations, we see hat the point x(t) + iy(t) lies on the hyperbola xy = c₁c₂. - Using the above guide lines find the streamlines of the flow associated with the complex function z² ?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
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Find the streamlines of the flows associated with the complex function Z
SOLUTION The streamlines corresponding to fi(z) = x - iy satisfy the system
dx
dy
dt
dt
x
and so x(t) = c₁e¹ and y(t) = c₂e¹. By multiplying these two parametric equations, we see
that the point x(t) + iy(t) lies on the hyperbola xy = C₁C₂.
Q3- Using the above guide lines find the streamlines of the flow associated
with the complex function Z ?
1
2
x² + y²
conjugate analytic function?
Q4- If u(x, y) =
-y
is harmonic function of v, check its analyticity and find its
Transcribed Image Text:Find the streamlines of the flows associated with the complex function Z SOLUTION The streamlines corresponding to fi(z) = x - iy satisfy the system dx dy dt dt x and so x(t) = c₁e¹ and y(t) = c₂e¹. By multiplying these two parametric equations, we see that the point x(t) + iy(t) lies on the hyperbola xy = C₁C₂. Q3- Using the above guide lines find the streamlines of the flow associated with the complex function Z ? 1 2 x² + y² conjugate analytic function? Q4- If u(x, y) = -y is harmonic function of v, check its analyticity and find its
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