Linearisability of Holomorphic Vector Fields and Poincaré-Dulac Normal Form

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Complex Algebraic Foliations, Book by A. Lins Neto and Bruno Scárdua, Chapter 1, Page 36.

The last two lines, Don't you think they should have written that the vector field is locally conjugate (instead of locally equivalent) in the singularity to a vector field in $\mathbb{C}^2$ of the form $(x,ny+x^n)$ (instead of $(x,ny+ax^n)$). The vector field will be linearisable if and only if $n=1$ (instead of $a = 0$).

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