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Question Number 167928 by Mastermind last updated on 29/Mar/22

$$Showthat\mid 1-i{\mid }^x=2^{x}hasnononzerointegralsolution$$

Answered by MJS_new last updated on 30/Mar/22

$$\mid 1-\mathrm{i}\mid =\sqrt{2};\mid 1-\mathrm{i}{\mid }^x={\left(\sqrt{2}\right)}^x=2^{\frac{x}{2}}$$$$2^{\frac{x}{2}}=2^x$$$$\left(2^{\frac{x}{2}}\right)={\left(2^{\frac{x}{2}}\right)}^2$$$$\Rightarrow 2^{\frac{x}{2}}=0\vee 2^{\frac{x}{2}}=1\Rightarrow x=-\mathrm{\infty }\vee x=0$$

Commented by Mastermind last updated on 31/Mar/22

$$Thanks$$

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