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harmonic conjugates

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harmonic conjugates [här′män·ik ′kän·jə·gəts]
(mathematics)
Two points,P3andP4, that are collinear with two given points,P1andP2, such thatP3lies in the line segmentP1P2whileP4lies outside it, and, ifx1,x2,x3, andx4are the abscissas of the points, (x3-x1)/ (x3-x2) = - (x4-x1)/(x4-x2).
A pair of harmonic functions,uandv, such thatu+ivis an analytic function, or, equivalently,uandvsatisfy the Cauchy-Riemann equations.


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