x2 t01 08 locus & complex nos 2 (2013)
TRANSCRIPT
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Locus and Complex Numbers
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Locus and Complex Numbers , find the locus of or f z z
given some condition for or z
![Page 3: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/3.jpg)
Locus and Complex Numbers , find the locus of or f z z
given some condition for or z(Make the condition the subject)
![Page 4: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/4.jpg)
Locus and Complex Numbers
or 0arg,0Imrealpurely is
, find the locus of or f z z given some condition for or z(Make the condition the subject)
![Page 5: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/5.jpg)
Locus and Complex Numbers
or 0arg,0Imrealpurely is
2
arg,0Reimaginarypurely is
, find the locus of or f z z given some condition for or z(Make the condition the subject)
![Page 6: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/6.jpg)
Locus and Complex Numbers
or 0arg,0Imrealpurely is
2
arg,0Reimaginarypurely is
linear functionarg locus is an arc of a circlelinear function
, find the locus of or f z z given some condition for or z(Make the condition the subject)
![Page 7: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/7.jpg)
Locus and Complex Numbers
or 0arg,0Imrealpurely is
2
arg,0Reimaginarypurely is
linear functionarg locus is an arc of a circlelinear function
2 if arcminor *
2 if arcmajor *
2 if semicircle *
, find the locus of or f z z given some condition for or z(Make the condition the subject)
![Page 8: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/8.jpg)
4,2
2 if of locus theFind ..
zzwwige
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zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw
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zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
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zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
12
w
z
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zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
12
w
z
4
12
w
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zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
12
w
z
4
12
w
41
2
w
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zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
12
w
z
4
12
w
41
2
w
211 w
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zzw 2
411 i.e.
21 radius and 1,0 centre circle, a is locus
22
yx
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
12
w
z
4
12
w
41
2
w
211 w
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realpurely is and 11 if of locus theFind w
zzwzii
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iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
![Page 18: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/18.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
![Page 19: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/19.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww
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iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
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iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
![Page 22: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/22.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
![Page 23: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/23.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
locus is 0, excluding 1,0y
1 0,bottom of fraction 0 z
![Page 24: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/24.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
locus is 0, excluding 1,0y
1 0,bottom of fraction 0 z
OR or 0argthen realpurely is If ww
![Page 25: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/25.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
locus is 0, excluding 1,0y
1 0,bottom of fraction 0 z
OR or 0argthen realpurely is If ww
or 011arg..
zzei
![Page 26: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/26.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
locus is 0, excluding 1,0y
1 0,bottom of fraction 0 z
OR or 0argthen realpurely is If ww
or 011arg..
zzei
or 01arg1arg zzy
x
![Page 27: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/27.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
locus is 0, excluding 1,0y
1 0,bottom of fraction 0 z
OR or 0argthen realpurely is If ww
or 011arg..
zzei
or 01arg1arg zzy
x1-1
![Page 28: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/28.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
locus is 0, excluding 1,0y
1 0,bottom of fraction 0 z
OR or 0argthen realpurely is If ww
or 011arg..
zzei
or 01arg1arg zzy
x1-1
![Page 29: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/29.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
locus is 0, excluding 1,0y
1 0,bottom of fraction 0 z
OR or 0argthen realpurely is If ww
or 011arg..
zzei
or 01arg1arg zzy
x1-1
![Page 30: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/30.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
locus is 0, excluding 1,0y
1 0,bottom of fraction 0 z
OR or 0argthen realpurely is If ww
or 011arg..
zzei
or 01arg1arg zzy
x1-1
locus is 0, excluding 1,0y
![Page 31: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/31.jpg)
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww 011.. yxyxei
0 yxyyxy
002
yy
locus is 0, excluding 1,0y
1 0,bottom of fraction 0 z
OR or 0argthen realpurely is If ww
or 011arg..
zzei
or 01arg1arg zzy
x1-1
locus is 0, excluding 1,0y : locus is 0, excluding 1,0 only
i.e. answer the original questionNote y
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64
arg if of locus theFind
zzziii
![Page 33: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/33.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
![Page 34: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/34.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
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64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x
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64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
![Page 37: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/37.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
![Page 38: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/38.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
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64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
(2,y)r
![Page 40: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/40.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
(2,y)r
30
![Page 41: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/41.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
(2,y)r
30
60tan2
y
![Page 42: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/42.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
(2,y)r
30
60tan2
y
3260tan2
y
![Page 43: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/43.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
(2,y)r
30
60tan2
y
3260tan2
y
32,2 is centre
![Page 44: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/44.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
(2,y)r
30
60tan2
y
3260tan2
y
32,2 is centre
222 322 r
![Page 45: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/45.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
(2,y)r
30
60tan2
y
3260tan2
y
32,2 is centre
222 322 r
4162
rr
![Page 46: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/46.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
(2,y)r
30
60tan2
y
3260tan2
y
32,2 is centre
222 322 r
4162
rr
points. theseincludingnotbut 4,0 and 0,0 joining chordby the formed 16322
circletheofarcmajor theislocus22
yx
![Page 47: X2 t01 08 locus & complex nos 2 (2013)](https://reader033.vdocuments.site/reader033/viewer/2022060116/557e78cfd8b42a03668b5160/html5/thumbnails/47.jpg)
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
(2,y)r
30
60tan2
y
3260tan2
y
32,2 is centre
222 322 r
4162
rr
points. theseincludingnotbut 4,0 and 0,0 joining chordby the formed 16322
circletheofarcmajor theislocus22
yx
Patel: Exercise 4N; 5, 6
Cambridge: Exercise 1F; 10 to 20
HSC Geometrical Complex Numbers Questions