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I am trying to learn complex analysis on my own and for this I have chosen Fundamentals of Complex Analysis by Saff and Snider. I am stuck at the last question in section 1.3 which is as follows.

For the linkage illustrated in the figure, use complex variables to outline a scheme for expressing the angular position, velocity and acceleration of arm c in terms of those of arm a.

As an attempt to the solution, this is what I have thought of so far.

Let the arm a be dictated by the complex variable Za, similarly Zb for b and Zc for c. Also since the distance between the bottom of a and c is fixed (a + b - c), we can say

Za + Zb = Zc + (a+b-c). (Parallelogram law)

However I am not sure of what comes next as I am not sure what Zb is. How can i proceed? To express Zc with respect to Za, I will somehow need to know what Zb is in terms of Za. But how do I do that?

SMK.

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# Learning Complex Analysis

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