POTW Cohomology Ring of Complement of Hyperplanes in Complex n-space

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Let $n \ge 1$ and $1 \le m \le n$. Suppose $\lambda_1,\ldots, \lambda_m : \mathbb{C}^n \to \mathbb{C}$ are $\mathbb{C}$-linearly independent linear functionals. For each abelian group $G$, determine the cohomology ring $$H^*(\mathbb{C}^n \setminus \bigcup_{k = 1}^m \ker \lambda_k ; G)$$