J.M. kindly proposed

ListVectorPlot[
List /@ Table[
{
{x, k*Sin[x]}
, {Re[k*x + I], -Im[k*x + I]}
}
, {k, {.01, .2, .4, .6, 1}}
, {x, -1.57, 1.57, .1}
] // Evaluate
, VectorStyle -> {Red, Brown, Blue, Pink, Purple}
, VectorPoints -> All
]


The y component of the vectors plotted along these curves should just be the same 1 everywhere but they aren't.

Is there any other way to portray a complex function's variation along a set of curves?

Oct 12 for example Can anyone please write code to equivalently plot a series of short lines from (x,k*sin[x]) to (x+.1*kx,ksin[x]+.1) for {x, -1.57, 1.57, .1} and {k, {.01, .2, .4, .6, 1}} with according colors {Red, Brown, Blue, Pink, Purple}

• I know it messes up the coloring, but does removing List /@  fix the scaling issue? Sep 19, 2017 at 10:30
• Yes that's where I started,but onmy real example Ineed the colur and no arrowheads to avoid overlaps.. I am wondering if there is a way to draw the (vector) line segments themselves from more primitive commands or to automate this example for a string of k, data1 = Table[{-1 - x^2 + y, 1 + x - y^2}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; data2 = Table[{-(1 + x - y^2), -1 - x^2 + y}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2}]; ListVectorPlot[{data1, data2}, VectorPoints -> 8, VectorStyle -> {Red, Blue}] Sep 19, 2017 at 13:57