VCE Specialist 3/4 Question Thread!

[IndefatigableLover]

Functions of a complex variable are functions that take complex numbers as arguments. It is the main area of study of Complex Analysis:

http://en.wikipedia.org/wiki/Complex_analysis

Euler's formula is

Nice! I know Euler's Formula is covered in Specialist 3&4 though do we actually cover 'Complex Analysis' in 3&4 or is it just limited to just Complex Numbers?

[Valyria]

Nice! I know Euler's Formula is covered in Specialist 3&4 though do we actually cover 'Complex Analysis' in 3&4 or is it just limited to just Complex Numbers?

This year's graduating specialist maths class of John Monash Science School had an entire SAC based around euler's formula. Although it's beyond the scope of the syllabus, the questions probably required fundamental knowledge for complex numbers, trigonometry and calculus.

[keltingmeith]

Nice! I know Euler's Formula is covered in Specialist 3&4 though do we actually cover 'Complex Analysis' in 3&4 or is it just limited to just Complex Numbers?

Euler's Formula is (regrettably...) NOT covered in specialist, but it is REALLY REALLY COOL, and if you want to learn about it anyway, I highly encourage doing so!

No form of analysis is covered in high school. At all. Trust me, you don't want to cover analysis in VCE.

[IndefatigableLover]

This year's graduating specialist maths class of John Monash Science School had an entire SAC based around euler's formula. Although it's beyond the scope of the syllabus, the questions probably required fundamental knowledge for complex numbers, trigonometry and calculus.

Oh really it's beyond the scope of the syllabus? Well I guess you learn something new everyday.. I've had a look at the past materials on Euler's Formula and it does mention those topics actually!

Euler's Formula is (regrettably...) NOT covered in specialist, but it is REALLY REALLY COOL, and if you want to learn about it anyway, I highly encourage doing so!

No form of analysis is covered in high school. At all. Trust me, you don't want to cover analysis in VCE.

Haha well I'll learning about it at school tomorrow LOL *cries*
Yeah the name kind of spooks me out so yeah.. not looking forward to it >.<

[keltingmeith]

Don't be scared of it - it's a very nice formula and easy to use. :3 Hell, the derivation of it is actually pretty easy, and covered in one of the first year maths units at Monash.

[IndefatigableLover]

Don't be scared of it - it's a very nice formula and easy to use. :3 Hell, the derivation of it is actually pretty easy, and covered in one of the first year maths units at Monash.

Haha that definitely makes me feel more reassured for tomorrow LOL (you see we have a two part analysis task on it but it's a 'learn as you go' type of analysis task so I have no idea what to expect you see :S)

[bts]

when i am given the cartesian equation: x^2 - y^2 = 1

i got the vector equation: r(t) = 2 sec (t)i + 2 tan (t)j, but how did they get the domain for t as (-pi/2, pi/2)

?

[lzxnl]

when i am given the cartesian equation: x^2 - y^2 = 1

i got the vector equation: r(t) = 2 sec (t)i + 2 tan (t)j, but how did they get the domain for t as (-pi/2, pi/2)

?

That vector equation and its domain only really give half the hyperbola

But anyway, what they did was to try find the largest domain on which sec t and tan t are continuous. In other words, the largest domain in which cos t is not zero. (-pi/2, pi/2) is one such domain

[Valyria]

Is it just me or are exam 2's really tough to finish on time?   I try reduce the time spent on MC but I'm always completing them within 40-45 minutes, any tips other than practice more?

[keltingmeith]

Is it just me or are exam 2's really tough to finish on time?   I try reduce the time spent on MC but I'm always completing them within 40-45 minutes, any tips other than practice more?

Do MC last, but also try to do a couple during reading time, and just put the answer into your short term memory to colour in once writing time starts.

[lzxnl]

Don't be scared of it - it's a very nice formula and easy to use. :3 Hell, the derivation of it is actually pretty easy, and covered in one of the first year maths units at Monash.

If any VCE students want a very simple proof, here it is.
Differentiate e^-ix * (cos x + i sin x) by product rule, treating i as a constant such that i^2 = -1
Of course, you just differentiated cis x / e^ix. And you should get 0 as all the factors should cancel perfectly
So you know this quotient is a constant. Sub in x = 0 and you see that this quotient is 1. Proof done.

[kinslayer]

https://proofwiki.org/wiki/Euler's_Formula

[juzza12]

A question from VCAA Specialist exam 2 2013. I have absolutely no idea how to approach part ii of this question, I get that the line segment is of y=x, my teacher suggested trial and error but otherwise I have no clue how to write the complex equation in terms of z conjugate. A worked solution of the exam stated the equation through pretty much recognition but I don't see it. Any help would be appreciated!

[kinslayer]

After you plot the four points, you should be able to see that they form a square.

Now draw the line going through and and also the line going through and . You can see they intersect at the origin but importantly, they intersect at right angles (because they are diagonals of a square).

From there, you should be able to see that, at any point along the line through and , the distance from to is the same as the distance from to .

That is: .

[juzza12]

After you plot the four points, you should be able to see that they form a square.

Now draw the line going through and and also the line going through and . You can see they intersect at the origin but importantly, they intersect at right angles (because they are diagonals of a square).

From there, you should be able to see that, at any point along the line through and , the distance from to is the same as the distance from to .

That is: .

Thanks but I'm still confused :/