IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: cashem'up on September 26, 2010, 12:15:26 pm

Title: COMPLEX NUMBERS
Post by: cashem'up on September 26, 2010, 12:15:26 pm: hey guys got this tough az question...please help exam in 20 days still havent finished course
A and B are points in an Argand diagram representing the complex numbers 1 and i. P is a point on the circle having AB as a diameter. If P represents the complex number z , find the value of
arg z-1/z-i if P is in

A)the first quadrant
B) the second quadrant
c) fourth quadrant

By the way P2 and P# Pg 248 Q9 just in case if u have da book
Title: Re: COMPLEX NUMBERS
Post by: astarmathsandphysics on September 26, 2010, 12:48:00 pm: Will answer when net speeds up. Really slow on my pc.
Title: Re: COMPLEX NUMBERS
Post by: cashem'up on September 26, 2010, 02:01:50 pm: sure thanx
Title: Re: COMPLEX NUMBERS
Post by: astarmathsandphysics on September 27, 2010, 09:47:41 am: Dont know what happened there
Title: Re: COMPLEX NUMBERS
Post by: astarmathsandphysics on September 27, 2010, 09:49:07 am: this one too
Title: Re: COMPLEX NUMBERS
Post by: astarmathsandphysics on September 27, 2010, 09:50:19 am: Can you also scan in the question? I want to be sure I understood it.
Title: Re: COMPLEX NUMBERS
Post by: Deadly_king on September 27, 2010, 10:23:32 am: Quote from: astarmathsandphysics on September 27, 2010, 09:50:19 am
Can you also scan in the question? I want to be sure I understood it.
Sorry.......i don't have a scanner :(

But he has written the question likewise. We just need to find arg((z-1)/(z-i)) in the three cases.

In other words : arg(z-1) - arg(z-i)
Title: Re: COMPLEX NUMBERS
Post by: astarmathsandphysics on September 27, 2010, 10:35:17 am: I thought it was z-1/z-1 but the answer is similar
Title: Re: COMPLEX NUMBERS
Post by: Deadly_king on September 27, 2010, 10:38:20 am: Quote from: astarmathsandphysics on September 27, 2010, 10:35:17 am
I thought it was z-1/z-1 but the answer is similar
I just modified my post.

I don't think it's the same.
Title: Re: COMPLEX NUMBERS
Post by: astarmathsandphysics on September 27, 2010, 10:41:15 am: I see. Much easier question. Will do it when I get home.
Title: Re: COMPLEX NUMBERS
Post by: Deadly_king on September 27, 2010, 10:44:23 am: Quote from: astarmathsandphysics on September 27, 2010, 10:41:15 am
I see. Much easier question. Will do it when I get home.

Ok .....thanks pal :)

The answers from the book are : (a) Half pie (b) Negative half pie (c) Negative half pie
Title: Re: COMPLEX NUMBERS
Post by: astarmathsandphysics on September 28, 2010, 09:09:43 am: Here are my answers.
Title: Re: COMPLEX NUMBERS
Post by: cashem'up on September 28, 2010, 03:36:34 pm: Quote from: astarmathsandphysics on September 28, 2010, 09:09:43 am
Here are my answers.

hey thanks alot will chek it.... yea i modified it.... m sorry my bad , its z-1/z-i
Title: Re: COMPLEX NUMBERS
Post by: Deadly_king on September 29, 2010, 05:47:22 am: Quote from: astarmathsandphysics on September 28, 2010, 09:09:43 am
Here are my answers.

I managed to get the answer for part (a).

I don't mean to be rude Sir, but I still don't understand how you did parts (b) and (c) :(

Would you mind to elaborate a bit more, please?
Title: Re: COMPLEX NUMBERS
Post by: astarmathsandphysics on September 29, 2010, 09:05:37 am: The method is basically the same The triangle in the circle is a right angled triangle. I also used z shapes and similar triangles.
Title: Re: COMPLEX NUMBERS
Post by: Deadly_king on September 29, 2010, 09:36:52 am: Quote from: astarmathsandphysics on September 29, 2010, 09:05:37 am
The method is basically the same The triangle in the circle is a right angled triangle. I also used z shapes and similar triangles.

Hmm.......I think I got it now :)

Although it's quite hard to believe having a negative value for argument in the second quadrant. But I guess I never did a similar question previously. That's why I find it surprising :-\

Thanks loads for your help :D
Title: Re: COMPLEX NUMBERS
Post by: astarmathsandphysics on September 29, 2010, 09:39:21 am: you can have a positve value. Add 2pi
Title: Re: COMPLEX NUMBERS
Post by: Deadly_king on September 29, 2010, 10:17:40 am: Quote from: astarmathsandphysics on September 29, 2010, 09:39:21 am
you can have a positve value. Add 2pi

Yupz........ :)