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- MHB
- Thread starter Taleb
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u+ v= (a+ c)+(b+ d)i. $|u+v|= \sqrt{(a+ c)^2+ (b+ d)^2}=$$\sqrt{a^2+ 2ac+ c^2+ b^2+ 2bd+ d^2}= $$ \sqrt{(a^2+ b^2)+ (c^2+ d^2)+ (2ac+2bd)}< \sqrt{1+ 1+ 2(ac+ bd)}< \sqrt{2+ 2(ac+ bs)}$

Can you prove that $ac+ bd$ is less than 1/2?

- #3

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MHB

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Problem 2) seems to be a lot harder. I found a sketch here of how to prove it by induction (again with $\sqrt2$ rather than $\sqrt3$).

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