Paradoxica
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Re: HSC 2016 4U Marathon
Under what conditions does the following hold ?:
Under what conditions does the following hold ?:
HSC 2016 MX2 Marathon (archive) (1 Viewer)
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Drsoccerball
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Paradoxica
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Re: HSC 2016 4U Marathon
Under what conditions does the following hold ?:
α and β are arbitrary complex numbers.
Let me rephrase that.?
Under what conditions does the following hold ?:
α and β are arbitrary complex numbers.
KingOfActing
lukewarm mess
Re: HSC 2016 4U Marathon
edit: sniped
Are alpha and beta complex or real numbers?Under what conditions does the following hold ?:
edit: sniped
Re: HSC 2016 4U Marathon
 try checking your answer with easy values of $\alpha,\beta$. Note that if $\alpha = 2$ and $\beta = 1$, the inequality in Paradoxica's post holds but the one in yours doesn't.$)
(Edit: I think you edited your inequality. Or I probably misread it before, thought it said less than or equal to, sorry.)
For anyone doing the Q., you can try interpreting the inequality in Paradoxica's post geometrically to gain some intuition if you want (the inequality says that the "scaled-to-unit-length" versions of the vectors alpha, beta in the complex plane are closer to each other than the original alpha and beta are).
(Edit: I think you edited your inequality. Or I probably misread it before, thought it said less than or equal to, sorry.)
For anyone doing the Q., you can try interpreting the inequality in Paradoxica's post geometrically to gain some intuition if you want (the inequality says that the "scaled-to-unit-length" versions of the vectors alpha, beta in the complex plane are closer to each other than the original alpha and beta are).
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Paradoxica
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Re: HSC 2016 4U Marathon
If anyone is attempting that question, try using a diagram, it is more helpful than you think.
If anyone is attempting that question, try using a diagram, it is more helpful than you think.
KingOfActing
lukewarm mess
Re: HSC 2016 4U Marathon
I'll diagram later but Is it |α|, |β| >= 1
I'll diagram later but Is it |α|, |β| >= 1
Paradoxica
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Paradoxica
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Re: HSC 2016 4U Marathon
There's also another set of conditions that exist when one of them is absolutely larger than 1, but I don't seem to be able to tease it out.
There's also another set of conditions that exist when one of them is absolutely larger than 1, but I don't seem to be able to tease it out.
123ryoma12
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Re: HSC 2016 4U Marathon
Help please.
http://i.imgur.com/OqALLPv.png
This is the answer
http://imgur.com/a/0mdmt
I understand finding the Angular Velocity for A but I don't understand why it's using angle PBO instead of angle PBC for the B.
Are you meant to use the angle which is acute and if the angular velocity makes the angle smaller then it's negative?
Help please.
http://i.imgur.com/OqALLPv.png
This is the answer
http://imgur.com/a/0mdmt
I understand finding the Angular Velocity for A but I don't understand why it's using angle PBO instead of angle PBC for the B.
Are you meant to use the angle which is acute and if the angular velocity makes the angle smaller then it's negative?
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