Suppose we have the plane with equation x+(1+i)y-2z=0. I would assume n=(1, (1+i),-2) is the normal vector, however, if I take the vector u=(0, 1-i, 1) contained in the plane, the scalar product u⋅n gives 2i-2≠0. How can I extract the normal vector from the implicit equation when it has complex coefficients?
2026-04-03 12:52:13.1775220733
How to find the normal vector to a plane with complex coefficients?
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