Prove the Triangle Inequality for Complex Numbers

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Prove the Triangle Inequality for Complex Numbers

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Комментарии
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Just had to do this with three complex numbers still holds. You're a lifesaver.

Stalfoes
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Just had to do this for reals. As you mentioned, helps to recall some identities for complex numbers. Thanks!

acdude
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I might actually need this for my exam, thank you !

b-rogr
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Thank you sir
You explained it in an amazing way 😊😊
Please suggest me a good number theory book for imo preparation

Maths_.
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Please make a separate video on (different ways to find range of a function)

Maths_.
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For all the comp sci people, modulus =/= modulo. I've been getting it wrong this whole time too but I'm not a mathematician or a comp scientist.

raulca
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6:05 how can you just put an inequality symbol on the entire equation and then go back to a normal equal sign ???

itachi
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At 6:47 why can we remove the conjugate symbol on Beta?

HORSE-E
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is this somehow related to Cauchy–Schwarz inequality |Re(z conjugate(w)| <= |z| |w| ?

Cpt.Zenobia
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I would've tried to write each complex number as a + bi, but I get the feeling it's more powerful to do it with conjugates as in the video. Where else do conjugates come up in proofs of complex numbers like this?

txikitofandango
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Could we also see the result quickly by thinking of complex numbers as vectors in a 2d Euclidean plane, and using the triangle inequality result from that normed vector space? Or is it the case that this alternate pathway requires a lot of setup?

wiggles