HSC Tips - Complex Numbers (2 Viewers)

[McLake]

Ok, 2nd in series of tip pages.

My biggest tip for complex numbers is don't be decived by how easy they appear. Many of the Q7/Q8 are harder applications of complex numbers.

And on to the tips:
- Know how to use De Moivres to do quetions like:
(cos(x))^n = something in terms of sin or cos
- Know how to do the "roots of unity" questions.
- Know how to factorise complex polynomials
- Be able to draw complex numbers into other topics

Any other tips or questions?

 

[Affinity]

- Know how to do arithmetic with complex numbers:
-- Using conjugates (eg for division, expanding)
-- Using roots of unity to find ALL nth roots
-- Using the polar form (mod/arg)
-- |xy| =|x||y|
-- arg(xy) = arg(x) + arg(y)
-- "multiply the modulus, add the arguments"

- Translate geometric relations into complex number equations (inequalities) and vice versa:
-- z represents a point
-- (|z-w| = k) is a circle centered at w and with radius k
-- (|z-a| = |z-b|) perpendicular bisector of a, b

- Translate unfamilar statements by changing z into x+iy

- Multiplying by cis(t) corrosponds to rotation of angle t about O

- Sometimes it helps to think of complex numbers as an ordered pair of 2 real numbers

- Learn to prove De Moivre's theorem, it's a question that will come up once in a while in the paper
EDIT: And know the defintion (in words) and how to prove it.

- Label argand plane Re and Im instead of x and y

- Polynomials and complex numbers are interrelated, usually you will have to discuss one with results in the other topic, try not to get in the habit of thinking in terms of topics, it's all maths.

- Complex numbers can be used to prove results in geometry, and is usually simpler than coordinate geometry. So you might try this if you just can't do a circle geometry question and have time left.

 

[Mathematician]

Complex numbers can be used to prove results in geometry, and is usually simpler than coordinate geometry. So you might try this if you just can't do a circle geometry question and have time left.

Q: Do one circle geometry Q using complex numbers please! I really thought U could do that, now its confirmed.

A: Many circle properties can be proved with Complex Numbers.

 

[Affinity]

ofcourse you can! some turns out nicely too.

 

[Mathematician]

...

hmmm.. i kinda asked for u to do one
Thx

 

[McLake]

Ok. I will do one tommorow ...

 

[freaking_out]

Originally posted by McLake
Ok. I will do one tommorow ...

 

[McLake]

Sorry. I can't seem to find one ...

 

[Affinity]

hmm.. I will post the proof on simpson's theorem ( last year's 4 b) tomorrow.

 

[TastesGoodBut]

and PLEASE revise how to turn into mod arg form... i lost 4 marks in one assessment, not because i didnt know how but because i didnt stop and think about it and did sum stupid thing

 

[freaking_out]

hey does complex numbers provide a systematic way of doing circular geometry problems???

 

[Affinity]

sort of.. if you are really desperate and have the time to spare

 

[freaking_out]

Originally posted by Affinity
sort of.. if you are really desperate and have the time to spare

well can u pls. post up some examples...so that i can do that if i am faced with this situation..

 

[Mathematician]

...

YEAH PLZ

I HATE CIRCLE GEOMETRY

 

[freaking_out]

come on, whats taking so long for someone to show us how to use complex numbers for circular geometry??? ....anyways, if u can't b bothered can u refer us to a website/textbook atleast?

 

[Mathematician]

..

Have they lied to us freaking_out

No im sure they tell the truth.

 

[freaking_out]

Re: ..

Originally posted by Mathematician
Have they lied to us freaking_out

No im sure they tell the truth.

i guess they don't wanna tell us coz that would mean their marks being affected due to us getttin' a few extra marks.

 

[KeypadSDM]

Re: Re: ..

Originally posted by freaking_out
i guess they don't wanna tell us coz that would mean their marks being affected due to us getttin' a few extra marks.

Exactly. How else do you think I got my ranking?

 

[freaking_out]

Originally posted by KeypadSDM
Exactly. How else do you think I got my ranking?

calm down u arrogant fool!

 

[Grey Council]

hey! he has reason to be proud. But I think it'd be more appreciated if people actually post up more tips. AND an example of how a circal geometry question could be done using complex numbers.