Question Complex No (1 Viewer)

[wololol]

If z= rcistheta and |z|=1, show cosntheta = [z^n+(1/(z^n))]/z and sinntheta = [z^n-(1/(z^n))]/(zi) if n is an integer.

not sure if i mixed up some 2s and zs there =P

yuh and also im not quite the complex number expert yet =P

 

[SpiralFlex]

First of all

Our first aim:

Now, we know that



But the modulus of z=1.


Also,





This can be extended for the general case with powers of n!


Immediately we should know that the cosine of z is the real part. So we would probably need to do something to manipulate it to that form.



We know the cosine function is even and the sine function is odd.








Now our aim:



By the same argument,

 

[wololol]

rep+ how do you write those mathematical symbols like that on the computer?

 

[rolpsy]

 

[SpiralFlex]

Also I remember doing this question from a past trial paper. James Ruse?

@OP, I use LAAAA tex. (Pronounced in a French accent. )

 

[wololol]

Also I remember doing this question from a past trial paper. James Ruse?

@OP, I use LAAAA tex. (Pronounced in a French accent. )

you got that right too (=

 

[SpiralFlex]

you got that right too (=

Yeah I have a good memory of that question when Spiral was a junior. It's also a common question too. So its worth noting me and Rolspies solutions.

 

[IamBread]

I think you mean

 

[rolpsy]

Yeah I have a good memory of that question when Spiral was a junior. It's also a common question too. So its worth noting me and Rolspies solutions.

btw I posted another question in the marathon
oh and how was scischool?

 

[SpiralFlex]

I think you mean

Typing on iPhone. >_>

 

[SpiralFlex]

btw I posted another question in the marathon
oh and how was scischool?

Put it this way....

(Dot dot dot)

My ticket was free anyway thanks to my stealing skills.

 

[wololol]

scischool? 8)

 

[SpiralFlex]

scischool? 8)

Don't wanna talk about it. *pouts*

 

[Carrotsticks]

Rolpsy's method is more efficient.

 

[zhiying]

^Agree, sorry Spiral