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I want to show, Image of $unit~ disc$ under a discontinuous linear functional from a Normed Linear Space is $\mathbb{C}$ . I know the Image is Unbounded

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    ${x\in X : ||x|| \le 1}$2011-03-18

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Hint: a discontinuous linear functional is still linear! So if $f(x)=z$, consider $f(wx)$, where $|w|=1$.