x2 t01 08 locus & complex nos 2 (2013)
TRANSCRIPT
Locus and Complex Numbers
Locus and Complex Numbers , find the locus of or f z z
given some condition for or z
Locus and Complex Numbers , find the locus of or f z z
given some condition for or z(Make the condition the subject)
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)
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)
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)
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)
4,2
2 if of locus theFind ..
zzwwige
zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw
zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
12
w
z
zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
12
w
z
4
12
w
zzw 2
4,2
2 if of locus theFind ..
zzwwige
2 zzw 21 wz
12
w
z
4
12
w
41
2
w
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
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
realpurely is and 11 if of locus theFind w
zzwzii
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
iyx
iyxiyxiyxw
11
11
realpurely is and 11 if of locus theFind w
zzwzii
22
22
1111
yxyyxiyxix
0Im then realpurely is If ww
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
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
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
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
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
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
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
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
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
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
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
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
64
arg if of locus theFind
zzziii
64
arg if of locus theFind
zzziii
64
arg
zz
64
arg if of locus theFind
zzziii
64
arg
zz
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
64
arg if of locus theFind
zzziii
64
arg
zz
6
4argarg zz
y
x4
6
axis below
4argarg
z-zNOTE:
2
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
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
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
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
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
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
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
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
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