28 Jan '04 10:49

...prelim time! 😀

i had my AH maths exam yesterday-it was good. a challenge. didn't get 2 questions, and i knew both of them too! one was the wording that got me...[start question]find the 4th roots of unity[end question]. the answer? (0=theta btw) cos0+isin0, cos(0+2pi)+isin(0+2pi), cos(0+4pi)+isin(0+4pi), cos(0+6pi)+isin(0+6pi). de moivres theorem. (well, i think that's the question anyway-but that's definatly the answer...and the other was i had to find the solutions for something along the lines of z^4+5(z^3)+12(z^2)+4z+52. they were all imaginary numbers, and we were already given one of them (2i, i think) so we knew 2 of them (2i, -21) and so we had to find the others. tisn't too hard 🙁

but anyway-a kinda clever little question i liked...o.k.-so it's the only other one i remebered, but it's a nice question...(the E is sigma-means to add up everything from k=1 to n...i couldn't find a sigma sign-sorry...😛)

n

E (4k+1)

k=1

write in terms of n.

i had my AH maths exam yesterday-it was good. a challenge. didn't get 2 questions, and i knew both of them too! one was the wording that got me...[start question]find the 4th roots of unity[end question]. the answer? (0=theta btw) cos0+isin0, cos(0+2pi)+isin(0+2pi), cos(0+4pi)+isin(0+4pi), cos(0+6pi)+isin(0+6pi). de moivres theorem. (well, i think that's the question anyway-but that's definatly the answer...and the other was i had to find the solutions for something along the lines of z^4+5(z^3)+12(z^2)+4z+52. they were all imaginary numbers, and we were already given one of them (2i, i think) so we knew 2 of them (2i, -21) and so we had to find the others. tisn't too hard 🙁

but anyway-a kinda clever little question i liked...o.k.-so it's the only other one i remebered, but it's a nice question...(the E is sigma-means to add up everything from k=1 to n...i couldn't find a sigma sign-sorry...😛)

n

E (4k+1)

k=1

write in terms of n.