X2 t01 12 locus & complex nos 3 (2012)

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 *

, 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 *

, 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

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

Exercise 4N; 5, 6

Exercise 4O; 3 to 10, 12, 13a, 14, 17, 20b, 21a, 22, 25, 26

HSC Geometrical Complex Numbers Questions