Complex vector space/Finite-dimensional/Real basis/Exercise

Let ${}V$ be a finite-dimensional vector space over the complex numbers, and let ${}v_{1},\ldots ,v_{n}$ be a basis of ${}V$. Prove that the family of vectors

$v_{1},\ldots ,v_{n}{\text{ and }}{\mathrm {i} }v_{1},\ldots ,{\mathrm {i} }v_{n}$

forms a basis for ${}V$, considered as a real vector space.

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