Author Topic: Complex number problem (Read 1981 times) Tweet Share

chid · « **on:** April 05, 2008, 03:27:58 pm »

I've got a question.

Arg(z)= $\pi$ /4 and Arg(z-3)= $\pi$ /2. Find Arg(z-6i)

I'm a little confused.

Thanks.

Mao · « **Reply #1 on:** April 05, 2008, 03:57:27 pm »

is that $\frac{n}{2}$ or $\frac{\pi}{2}$ ??

i've just tried to use "n", and it was fruitless....

kj_ · « **Reply #2 on:** April 05, 2008, 04:01:42 pm »

i just -have- to post this; does anyone else notice:

the post was on:

Quote

Complex number problem
« on: Today at 03:27:58 PM »

the reply from mao was on:

Quote

Re: Complex number problem
« Reply #1 on: Today at 03:57:27 PM »

Mao · « **Reply #3 on:** April 05, 2008, 04:05:22 pm »

assuming you meant $\frac{\pi}{2}$

let $z=x+yi$

(and for the sake of being pedantic, thanks dcc)

$z-3=|z-3|cis(Arg(z-3))$

$\implies |z-3|\cos(Arg(z-3))+i \cdot |z-3|\sin(Arg(z-3))$

$\therefore Re(z-3)=|z-3|cos(Arg(z-3))$

$\implies Arg(z-3)=\cos^{-1}\frac{Re(z-3)}{|z-3|}$

$Arg(z-3)=\cos^{-1}\frac{x-3}{|z-3|}=\frac{\pi}{2}$

$\implies \frac{x-3}{|z-3|}=0$

$\implies x-3=0$ as $|z-3|>0$

$\implies x=3$

$Arg(z)=\frac{\pi}{4}$

$\implies y=x=3$

$Arg(3+3i-6i)=Arg(3-3i)=-\frac{\pi}{4}$

Mao · « **Reply #4 on:** April 05, 2008, 04:07:19 pm »

Kj_:
this question has been around for a little while:
http://vcenotes.com/forum/index.php/topic,2340.msg34537.html#msg34537

just that chid wanted a bit more "coverage" and I happened to look at it at the right time xD

and this one's gap is even less:

Quote from: http://vcenotes.com/forum/index.php/topic,2785.0.html

Parametric Curves
squance « on: Today at 02:49:15 PM »

Re: Parametric Curves
Mao « Reply #1 on: Today at 03:00:59 PM »

chid · « **Reply #5 on:** April 05, 2008, 05:54:42 pm »

Thanks Mao.

And yeah it was supposed to be pi as opposed to n.

How do you use all the mathematical symbols?

Mao · « **Reply #6 on:** April 05, 2008, 07:16:02 pm »

LaTeX:
http://vcenotes.com/forum/index.php/topic,864.0.html

a good guide to specific symbols:
http://www.artofproblemsolving.com/LaTeX/AoPS_L_GuideSym.php
(formats like integrals, radicals and matrices are found under "command" link on the same page)

evaporade · « **Reply #7 on:** April 06, 2008, 12:22:39 pm »

Arg(z-3)=pi/2, .: z-3=0+ai, .: z=3+ai.
Arg(z)=pi/4, .: z=b+bi.
.: b=a=3 and z=3+3i.
.: z-6i=3-3i, Arg(z-6i)=artan(-3/3)=-pi/4

Collin Li · « **Reply #8 on:** April 06, 2008, 08:04:02 pm »

Quote from: kj_ on April 05, 2008, 04:01:42 pm

i just -have- to post this; does anyone else notice:

the post was on:
Quote
Complex number problem
« on: Today at 03:27:58 PM »

the reply from mao was on:
Quote
Re: Complex number problem
« Reply #1 on: Today at 03:57:27 PM »

What do you mean? 30 minutes after... so what?

AppleXY · « **Reply #9 on:** April 11, 2008, 03:12:33 pm »

LOL.

The numbers are the same, only in different positions. (well, nearly the same)

:27 minutes --> :27 secs
:58 secs --> :57 minutes.

ed_saifa · « **Reply #10 on:** April 11, 2008, 03:36:22 pm »

I think he was insinuating how long Mao took.XD

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