complex no (1 Viewer)

[martin310015]

can some one help me out

let w= cos8+isin8 and z=w+1/w-1

show that z=-i cot8 8 = theta

Thanx

 

[wogboy]

Tip: Use @ for theta rather than the number 8.

Are you trying to prove
w = cos@ + isin@ and z = w + 1/w - 1,
so then z = -icot@ ?

It's not true, e.g:

let @ = pi/2,
then w = i
so z = i + 1/i - 1 = -1

but -icot@ = 0

-1 =/= 0

 

[martin310015]

what i got is icot @ from using the half angles.

 

[:: ck ::]

100bux says u go to prior

questoin 7a from the homework stop cheating

btw theres a correction its supposed to be 2@
double angle

 

[ae]

i think the question suppose to read
"w = cos2@ + isin2@ and z = w + 1/w - 1"

then its easy to prove z=-icot@

 

[martin310015]

thanx

 

[Mill]

$200 says I'm his class tutor, stop cheating Martin L

 

[Mill]

Actually I put the question in the worksheet.

Originally it was meant to be w = cos@ + isin@, but I decided that was to hard to simplify / work out (the answer in that case would be -icot[@/2] ). I guess it just wasn't fixed up in the homework sheet.

There's an alternative method of solving it, but its much more boring. You just realise the denominator. It's just a straightforward algebra bash that way.

 

[martin310015]

hahahaha
its not really cheating
no one posted the working outs

its the workin out that counts right...

 

[martin310015]

but shouldn't the answer be positive icot@/2 ........
for w=cos@+isin@

 

[Mill]

Yeah for the question written in the actual homework the answer you should get is -icot@/2. But the question written in the homework was wrong.

It should have been w=cos2@+isin2@, to give the answer of -icot@.

I'm fairly sure I changed it in your book, but marked it right anyway since you got -icot@/2 if I'm not mistaken.

 

[martin310015]

ok thanx

 

[Grey Council]

So Mill's is a tutor at Prior. mmm

How about you post up some questions, Mills?

 

[Mill]

Haha the qood questions I've found or created in the last few months have found their way into Prior worksheets, so I gots nothing for ya!

 

[Grey Council]

so what? post those questions up.

 

[martin310015]

mill do u do workshops tutoring

 

[martin310015]

i got a question
use mathematical induction to prove that the |z^n|=|z|^n

for this question how would i start it and do i use the modulus argument form or x+iy

 

[shkspeare]

haha and u kno how much prior sheets are worth guardian? lolz i dun think ppl wud like it if it was given out

 

[Mill]

I have 1 workshop haha. I didn't want any, and I think as soon as your 4u class gets more people I won't have the workshop anymore. My 1 workshop is at the end of your class (like during the end of it) so you won't be able to be in it.

 

[Mill]

Just looking at it I'd try mod-arg form first since if z = rcis@, then |z| = r, which is nice and simple. I'll check it now though.