Question 570021
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Rhombus diagonals bisect each other, so if the diagonals lie on the axes, then the opposite vertices (the endpoints of the diagonals) are equidistant from the origin.  Further, the vertices must lie on the axes as well, so you only need two variables for the 4 vertices.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(a,\,0\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(-a,\,0\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(0,\,b\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(0,\,-b\right)]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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