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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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What it is $unit dis$? Is it the unit sphere or the unit ball? – shuhalo Mar 18 '11 at 9:59
${x\in X : ||x|| \le 1}$ – SION Mar 18 '11 at 10:04

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

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