How to perfect Complex Numbers? (1 Viewer)

[hit patel]

Guys as you know that there is atleast one complex number question in an exam that is completely different to what we have done in most trial papers or is not in the books whether it may be roots of unity or trig applications in complex numbers. Is there a way to familiarise each and every question? Is tehre a book such as so that gives you each type of question that may be in the exam. The proofs in complex numbers are much more different to what I have done when I checked some trial past papers from JRAHS.
Thanks

 

[braintic]

Could this please be moved to the Extension 2 forum.

 

[obliviousninja]

Guys as you know that there is atleast one complex number question in an exam that is completely different to what we have done in most trial papers or is not in the books whether it may be roots of unity or trig applications in complex numbers. Is there a way to familiarise each and every question? Is tehre a book such as so that gives you each type of question that may be in the exam. The proofs in complex numbers are much more different to what I have done when I checked some trial past papers from JRAHS.
Thanks

What section within complex?

 

[Sy123]

Guys as you know that there is atleast one complex number question in an exam that is completely different to what we have done in most trial papers or is not in the books whether it may be roots of unity or trig applications in complex numbers. Is there a way to familiarise each and every question? Is tehre a book such as so that gives you each type of question that may be in the exam. The proofs in complex numbers are much more different to what I have done when I checked some trial past papers from JRAHS.
Thanks

Mathematics is not about learning each type of question and then using your knowledge on what to do for each one, maybe this is more common in 2U maths.

But 4U maths, especially at HSC level (probably not at school level due to quality), they will largely have different types of questions here and there, and that's where you need to use your intuition and understanding of the concepts.

For things like complex numbers and many other topics bar harder 3U, it comes down to less intuition and more understanding the concepts.

To develop understanding you need to really engage with the topic well, you need to understand what vectors are, what they mean etc etc

Developing intuition simply comes off developing problem solving skills, being able to simplify the problem, to understand where you're going with the question, what the question is asking and sometimes simply 'seeing' the answer. Though this sort of skill is really only needed in Q16 and maybe Q15, the rest of the exam is very doable if one understands all concepts to its fullest extent

 

[HSC2014]

A wise man once told me "a smart student does not need to do a thousand questions unlike a (dumb) student". I see your ATAR goal is 99.95; consider this: there are people who have finished the year 12 math course before even starting the year (international, accelerated) - what chance do you have to take them on if you choose to rely on experience and not understanding?

 

[hit patel]

Mathematics is not about learning each type of question and then using your knowledge on what to do for each one, maybe this is more common in 2U maths.

But 4U maths, especially at HSC level (probably not at school level due to quality), they will largely have different types of questions here and there, and that's where you need to use your intuition and understanding of the concepts.

For things like complex numbers and many other topics bar harder 3U, it comes down to less intuition and more understanding the concepts.

To develop understanding you need to really engage with the topic well, you need to understand what vectors are, what they mean etc etc

Developing intuition simply comes off developing problem solving skills, being able to simplify the problem, to understand where you're going with the question, what the question is asking and sometimes simply 'seeing' the answer. Though this sort of skill is really only needed in Q16 and maybe Q15, the rest of the exam is very doable if one understands all concepts to its fullest extent

Thanks

A wise man once told me "a smart student does not need to do a thousand questions unlike a (dumb) student". I see your ATAR goal is 99.95; consider this: there are people who have finished the year 12 math course before even starting the year (international, accelerated) - what chance do you have to take them on if you choose to rely on experience and not understanding?

There is a clear stereotype there: accelerants = smart people. Consider This: Einstien was not an accelerant nor was he a Grade 6 Graduated Student, however what do we consider him as today- Genius. Similarly, I donot compete with other people and I absolutely detest that. My only Aim is to get as the highest there is: If you aim for the moon and miss, you will land on the stars. Anyways the point is that my question referred to the fact that practice=understanding. I have understanding but applying it is the only thing that I must improve on. Now can you actually tell me how to perfect it because I understand the concepts.

Thanks

 

[HSC2014]

There is a clear stereotype there: accelerants = smart people. Consider This: Einstien was not an accelerant nor was he a Grade 6 Graduated Student, however what do we consider him as today- Genius. Similarly, I donot compete with other people and I absolutely detest that. My only Aim is to get as the highest there is: If you aim for the moon and miss, you will land on the stars. Anyways the point is that my question referred to the fact that practice=understanding. I have understanding but applying it is the only thing that I must improve on. Now can you actually tell me how to perfect it because I understand the concepts.

Thanks

Yes my point exactly; you will lose to accelerators if you choose to play their own game of experience. They are not necessarily intelligent.
I don't know you interpreted my response but simply that to get 99.95 you have to... beat everyone.

"Is there a way to familiarise each and every question? Is tehre a book such as so that gives you each type of question that may be in the exam. The proofs in complex numbers are much more different to what I have done when I checked some trial past papers from JRAHS."

It sounded like you were asking for help outside the field of understanding concepts but supposedly I am wrong so there is nothing further I can contribute as guidance. Let it help others though. Sorry if you misinterpreted.

 

[hit patel]

Yes my point exactly; you will lose to accelerators if you choose to play their own game of experience. They are not necessarily intelligent.
I don't know you interpreted my response but simply that to get 99.95 you have to... beat everyone.



It sounded like you were asking for help outside the field of understanding concepts but supposedly I am wrong so there is nothing further I can contribute as guidance. Let it help others though. Sorry if you misinterpreted.

Thanks for the Tips anyways. No Problem.

 

[seanieg89]

Doing a mass amount of questions is a much less effective (and imo infinitely less fun) way of developing understanding than doing fewer harder questions slowly and really analysing your thought processes afterwards. There is a lot more to understanding a particular concept than learning the definitions and the theorems, you need to learn how this area interacts with other parts of mathematics.

Eg.
Why are the theorems true?
Is there a way of visualising the concept?
What kind of thing will it be useful to solve? Why?
Is there any alternative way of dealing with things that this can solve?
What are the advantages/disadvantages of the alternatives?
Is there a way of expressing this concept in a different area of mathematics?
Play around with things, if you learn a new theorem, see what you can prove yourself using this theorem. It's really important to know the strengths and limitations of your tools.


Once you properly understand concepts, then nothing in MX2 should really pose a challenge given enough time...then you can worry about the silly little things like speed and avoiding calculation errors. The problem is that too many students who think they understand concepts really don't, and are actually "mimicking" rather than thinking.