2007 hsc question (1 Viewer)

[yorkstanham]

hey, i need help with question 2 (c) and 2 (d) part (iii) on the 2007 ext 2 hsc

thanks in advance

 

[buchanan]

Terry Lee's solutions are up at

http://www.hsccoaching.com/Resources/2007 Ext2.pdf

and itute's ones are at

http://www.itute.com/mathline/nsw_bos_maths_ext2_sol2007.pdf

 

[proringz]

For question 2 c (this was a question for test I did last week lol)

1/Z + 1/ Z bar = 1

Substi. z = x + iy

1/(x+iy) + 1/(x-iy) = 1

Cross multiply you get:

(x+iy)+(x-iy)/(x+iy)(x-iy) = 1

2x/x^2+y^2 = 1

multiply to both sides

2x = x^2 + y^2

subtract 2x to other side, you get x^2-2x+y^2 =0

Complete the square you get

(x-1)^2 + y^2 = 1

Therefore, locus is circle with centre (1, 0) with radius 1

question 2d cant be stuffed lol