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October 04, 2025, 08:50:36 am

Author Topic: Momo's Spech Hw help trend !  (Read 3321 times)  Share 

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the.watchman

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Re: Momo's Spech Hw help trend !
« Reply #30 on: February 04, 2010, 06:43:07 am »
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Just wondering, is it possible to use Laplace expansion to work out when the system of equations has none or infinite solutions in this situation?

Yes, you can. In SM, you are welcome to use methods beyond the syllabus, so long as you get to the right answer via a correct method.

However, Laplace expansion [i.e. determinant] does not give information about whether the system has no solutions or infinite solutions. It simply states 'unique solution' or 'no unique solutions'. Gaussian elimination is still a far better choice.

Ok, thanks for that Mao!
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Momo.05

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Re: Momo's Spech Hw help trend !
« Reply #31 on: February 20, 2010, 11:12:22 am »
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Hey once again, i need some help :)

Im doing complex numbers instead and atm im quite confuse on how to solve this question

If z = 1 + i.root3

Hence then find conjugate of z^-5 in Cartesian form ..?

THANK YOU! :)



fady_22

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Re: Momo's Spech Hw help trend !
« Reply #32 on: February 20, 2010, 11:34:42 am »
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Hey once again, i need some help :)

Im doing complex numbers instead and atm im quite confuse on how to solve this question

If z = 1 + i.root3

Hence then find conjugate of z^-5 in Cartesian form ..?

THANK YOU! :)




Change the complex number z into polar form: z=2cis(pi/3)
Using De Moivre's theorem, z^-5=(2cis(pi/3))^-5= 1/32 cis(pi/3)
The conjugate is 1/32cis(-pi/3)
Change this back into cartesian: z^-5=rcosx+rsinx.i=1/32.1/2+1/32.-sqrt(3)/2
=
« Last Edit: February 20, 2010, 11:45:32 am by fady_22 »
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Momo.05

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Re: Momo's Spech Hw help trend !
« Reply #33 on: February 20, 2010, 11:38:30 am »
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OHH thank you :)
I got it now ! ~

Momo.05

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Re: Momo's Spech Hw help trend !
« Reply #34 on: February 20, 2010, 11:57:20 am »
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Ohh another question, can someone check if w=root2(cis(pi/4)) equals to 1 + i in Cartesian form? Since thats what i got .. is it right? O.O

GerrySly

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Re: Momo's Spech Hw help trend !
« Reply #35 on: February 20, 2010, 12:28:19 pm »
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Stroodle

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Re: Momo's Spech Hw help trend !
« Reply #36 on: February 20, 2010, 12:29:36 pm »
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Ohh another question, can someone check if w=root2(cis(pi/4)) equals to 1 + i in Cartesian form? Since thats what i got .. is it right? O.O

Yeah, it's correct:








Momo.05

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Re: Momo's Spech Hw help trend !
« Reply #37 on: February 20, 2010, 01:56:01 pm »
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Phew, thanks ! :)

Momo.05

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Re: Momo's Spech Hw help trend !
« Reply #38 on: February 20, 2010, 04:17:05 pm »
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Okay, ive been stuck on this question for so long, can someone out there help me with it ? PRETTY PLEASE !? ITS DRIVING ME NUTS ATM!

By considering z = cis(x) and z - z^-1 find the expression for sin3x in terms of sinx

I tired using (z -z^-1)^3 but i dont understand where im going wrong... =="

THANK YOU FOR THE HELP!!

Mao

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Re: Momo's Spech Hw help trend !
« Reply #39 on: February 20, 2010, 11:59:08 pm »
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Expanding:



Expanding

Substituting polar forms:

Simplifying:



« Last Edit: February 21, 2010, 12:01:04 am by Mao »
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