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Thanks for the help, but I'm lost after the root.

z1 and z2 are two complex numbers whose argument differ by 90 degrees. Prove mod (z1 + z2) = mod (z1 - z2) I know this has something to do with complex conjugates, but I dunno how to apply it,

Thanks for the help, but the answer says its r=1-\frac{1}{\sqrt[3]{\Theta +1}}

Hi. I'm fairly good in doing these types of questions but this one is different because of the way it is arranged. I've tried to flip it but it still doesn't work. Given\ \frac{d\Theta }{dr}=\frac{3}{(1-r)^3}, and\ that\ r(0)=0, find\ r\ in\ terms\ of\ \Theta.\ Use\ the\ substitution\ u=1-r

Hi. I'm having trouble on some integration. These are from the 2 U Fitzpatrick Book. 12. A hemispherical bowl of radius a units is filled with water to a depth of a/2 units. Find, by integration, the volume of the water. 18. The region bounded by the curve x^1/2 + y^1/2 = 2 and the...

Another question here. If x=cos^2\Theta show that the roots of the equation 32x^3-48x^2+18x-1=0 are cos^2\frac{\pi }{12}, cos^2\frac{5\pi }{12},cos^2\frac{9\pi }{12}

thanks very much

Thanks for all the help guys. One more quick thing. Can someone help me prove this. z^n+\frac{1}{z}=2cosn\Theta PS. That 1/z is meant to be 1/z^n

Using Doivire's Theorem, find the cube roots of 8. How would I do that?

Sorry for the questions guys. I need to fine tune this complex number stuff. How would you find the relation between x and y if z=x+iy

Also, is there any relationship between the modulus and argument of z and 1/z

Thanks study freak. I get the steps of what you're doing, but can you tell me the Trig identities you used.

Sorry I'm not really good with Trig. Can you explain each of the formulas used for the step.

Thanks for the comment but I'm still unsure how to do this. For example find the modulus and argument of 1+cos\frac{\pi }{3}+isin\frac{\pi }{3} using Trig rather than expanding the whole thing, which sometimes gets very messy.

I've got a quick query here. How would I find the modulus and argument of something like this 1+cos\Theta +isin\Theta

Thanks for the reply. Regarding the Excel one, is it a textbook or is it a questions book?

Hi. I was wondering if there are any good textbooks out there based mainly on questions. I know there is the dot point book but what else?

Hi. Since in the HSC there is only assumed knowledge required for the preliminary course, is it necessary to make long detailed notes for the course? For example, in Physics, should you make notes for the prelim syllabus as well as the HSC?

Hi. My physics test is coming up and I was wondering if anybody had some past physics exams. If you do, could you post it and I'd greatly appreciate it.

thanks guys. can someone explain question 3 for me cauz i still dont get it.