ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Biceps on November 11, 2012, 01:03:10 pm

Title: 2004 question 4) e) and f)
Post by: Biceps on November 11, 2012, 01:03:10 pm: How on earth do we do those questions. It is questions like these that worry me about VCAA complex number questions :/
Title: Re: 2004 question 4) e) and f)
Post by: polar on November 11, 2012, 01:21:13 pm: It passes through Q which is $-1 -2i$ , and also, since w is a complex number, it can be written in the form $w = x + yi$

$\begin{aligned} wz + \bar{w}\bar{z} &= 0 \\ (x+yi)(-1-2i) + (x-yi)(-1+2i) &=0 \\ -2x+4y &=0 \\ y &= \frac{x}{2} \\ \text{Let \;} x=2, y&= \frac{2}{2} \\ &=1 \end{aligned}$

Therefore, a possible $w$ is $w = 2 + i$
Title: Re: 2004 question 4) e) and f)
Post by: Biceps on November 11, 2012, 01:32:26 pm: Oh ok i get it now thanks :D
Title: Re: 2004 question 4) e) and f)
Post by: Somye on November 11, 2012, 01:37:59 pm: for f)

$MQ.DQ = 0$ , and going back to our theory that an angle subtended by the diameter of a circle = 90 degrees

DM = diameter = $2r = 4 - \frac{-9} {5}$
therfore $r = 29/10$

centre of circle = $D + r = \frac{11} {10}$

and so $T=$ { $z:|z-1.1| \leq 2.9,z \in{C}$ }
Title: Re: 2004 question 4) e) and f)
Post by: Biceps on November 11, 2012, 01:46:57 pm: Thanks a lot.
I actually used this method in an earlier question to find d. in d) ii) what was the right way of doing that one?