Question: Consider the ordinary vectors in three dimensions with complex components. (a) Does the subset of all vectors with a z = 0 constitute a vector

Consider the ordinary vectors in three dimensions

with complex components.
(a) Does the subset of all vectors with a_z = 0 constitute a vector space? If so, what is its dimension; if not, why not?
(b) What about the subset of all vectors whose z component is 1?
(c) What about the subset of vectors whose components are all equal?

(ax + ay + ak),

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