What is the lower bound of the complex function defined in the open unit disk $|z|<1$ with $f(z)=\Re(\sqrt{1-z^4})$ ? At which point the minimum is reached.
Please help me to solve this.
Finding lower bound of complex function
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complex-analysis
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0Hint: the set of values taken by $z^4$ and the set of values taken by $z$ on the unit disk are the same. Thus your problem is the same as for $f(z)=\Re(\sqrt{1-z})$. – 2017-02-13
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0@JeanMarie The point of the minimum will not change with $z^4\to z$.? – 2017-02-13
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0@MyGlasses Yes because, $z\mapsto z^4$ is surjective (=onto) from the unit open disk onto itself (besides, not injective) – 2017-02-13