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Say for example a question deals with a curve in the complex plane but the only technique required to solve the problem is algebraic manipulation (albeit perhaps using complex numbers) and the user merely wants help doing the algebraic manipulation.

Should the complex-analysis tag be used nonetheless instead of the algebra-precalculus tag?

Say for example a question deals with finding a map with particular predefined properties from one manifold to another of the same dimension and the user has already made progress on the conceptual and geometric front such that the only work that's left in order to produce the desired map is algebraic manipulation.

Should the differential geometry tag be used nonetheless instead of the algebra-precalculus tag?

Here is an example of a question whose initial tags were later replaced with algebra-precalculus by a more experienced user: Proving $\Im([\tan(\frac{m\pi}{2n+1})+i]^{2n})=\tan(\frac{m\pi}{2n+1})\Re([\tan(\frac{m\pi}{2n+1})+i]^{2n})$ for integers m and n

The work done by the OP involved using a known result about a particular type of algebraic plane curve in order to derive an equation.

After deriving their equation, the OP simply wanted help deriving a stronger result using the equation that the OP had already derived. The OP suspected that only algebraic manipulation of their already-existing equation would be needed in order to derive the stronger result.

Despite complex numbers being involved and despite the fact that the OP used a known result about a particular type of algebraic plane curve, I do find the tag algebra-precalculus appropriate, since algebraic manipulation is all that a user would need to do in order to help answer the question.

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"Algebra" and "Precalculus" are course titles / descriptions commonly used in the American educational system, primarily used in secondary schools. The tag refers to those courses and the content therein, and not any particular mathematical topic or field ("precalculus" is not a field of mathematics). Hence the tag should be used to indicate that the question is geared towards the material that a high school (or first year college) student is learning.

This tag is quite inappropriate for the question linked above.

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