Trig/complex question

[NE2000]

1st or 2nd quadrant for A

Show that

So I went about this by trying to find

But I get as my final answer instead of . I can't pinpoint what I've done

EDIT: I can also do this question by solving for x as a quadratic, but I would still like someone to explain why the first method isn't working

[kurrymuncher]

no, you're over complicating it.

sub x in as cisA. the reciprocal of cisA is just cis(-A), which is cosA -isinA

therefore

it is cosA + isin A +cosA - isinA= 2cosA

is that what you were after?

[NE2000]

I think the question wants you to prove x=cis(A) given the information in the first line above.

But still your method works I'm still hoping to find why my method above didn't work...

[kamil9876]

I think kurrymuncher's method really shows that x=cis(A) is a solution, but doesn't show that it is neccesarily the solution, e.g: x^2=4, well by plugging in x=2 you get a correct statement but that doesn't mean that x=2 was neccesary, since x=-2 was possible.

And NE2000. Think about this: , if you make the substitution you get:  which has the exact same structure as the first equation!, only different notation. This means that if x solves this equation then so does 1/x. However maybe one solution may be ruled out by using the info that it's 1st or second quadrant, cbf thinking any further

Just fill me in on the details of your solution, because i don't really know what you did, the statement you have provided is correct, (because first of second quadrant).

[humph]

Just let , substitute it in, and equate real and imaginary parts.