Locus and Complex Numbers

Locus and Complex NumbersCircles

y

x

R

R

R

R

2Rzz

Locus and Complex NumbersCircles

y

x

R

R

R

R

Rz or

2Rzz

Locus and Complex NumbersCircles

y

x

Ry

xR

R

R

Rz or

2Rzz

R

2Rzz

Locus and Complex NumbersCircles

y

x

Ry

xR

R

R

Rz or

2Rzz

R

Rz or

2Rzz

e.g. (i) Express these circles in terms of z

16 a) 22 yx

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

16zz

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

16zz

01246 b) 22 yxyx

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

16zz

01246 b) 22 yxyx1246 22 yyxx

2523 22 yx

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

16zz

01246 b) 22 yxyx1246 22 yyxx

2523 22 yx523 iz

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

16zz

01246 b) 22 yxyx1246 22 yyxx

2523 22 yx523 iz

252323 iziz

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

16zz

01246 b) 22 yxyx1246 22 yyxx

2523 22 yx523 iz

252323 iziz(ii) Find the centre and radius of;

25 a) iz

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

16zz

01246 b) 22 yxyx1246 22 yyxx

2523 22 yx523 iz

252323 iziz(ii) Find the centre and radius of;

25 a) iz 5,1 :centre

units 2 :radius

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

16zz

01246 b) 22 yxyx1246 22 yyxx

2523 22 yx523 iz

252323 iziz(ii) Find the centre and radius of;

25 a) iz 5,1 :centre

units 2 :radius

4944 b) iziz

e.g. (i) Express these circles in terms of z

16 a) 22 yx4z

16zz

01246 b) 22 yxyx1246 22 yyxx

2523 22 yx523 iz

252323 iziz(ii) Find the centre and radius of;

25 a) iz 5,1 :centre

units 2 :radius

4944 b) iziz 14:centre ,

units7:radius

izz 23 c)

izz 23 c)

izz 23

2222 1299 yxyx

izz 23 c)

izz 23

2222 1299 yxyx124499 2222 yyxxyx

52848 22 yyxx

izz 23 c)

izz 23

2222 1299 yxyx124499 2222 yyxxyx

52848 22 yyxx

85

41

21 22 yyxx

izz 23 c)

izz 23

2222 1299 yxyx124499 2222 yyxxyx

52848 22 yyxx

85

41

21 22 yyxx

6445

81

41 22

yx

izz 23 c)

izz 23

2222 1299 yxyx124499 2222 yyxxyx

52848 22 yyxx

85

41

21 22 yyxx

6445

81

41 22

yx

81

41 :centre ,

units 8

53 :radius

izz 23 c)

izz 23

2222 1299 yxyx124499 2222 yyxxyx

52848 22 yyxx

85

41

21 22 yyxx

6445

81

41 22

yx

81

41 :centre ,

units 8

53 :radius

02d) zzzz

izz 23 c)

izz 23

2222 1299 yxyx124499 2222 yyxxyx

52848 22 yyxx

85

41

21 22 yyxx

6445

81

41 22

yx

81

41 :centre ,

units 8

53 :radius

02d) zzzz0422 xyx

42 22 yx

izz 23 c)

izz 23

2222 1299 yxyx124499 2222 yyxxyx

52848 22 yyxx

85

41

21 22 yyxx

6445

81

41 22

yx

81

41 :centre ,

units 8

53 :radius

02d) zzzz0422 xyx

42 22 yx 02:centre ,

units2:radius

Lines

Lines y

x

c

cz Im

Lines y

x

y

x

c

cz Im

k

kz Re

Lines y

x

y

x

c

cz Im

k

kz Re

y

x

Lines y

x

y

x

c

cz Im

k

kz Re

y

x

1

2

Lines y

x

y

x

c

cz Im

k

kz Re

y

x 21 zz

1

2

izizge 21..

2222 1211 yxyx

izizge 21..

2222 1211 yxyx12441212 2222 yyxxyyxx

izizge 21..

2222 1211 yxyx12441212 2222 yyxxyyxx

0346 yx

izizge 21..

2222 1211 yxyx12441212 2222 yyxxyyxx

0346 yx

1,2and1,1 ofbisector OR

izizge 21..

2222 1211 yxyx12441212 2222 yyxxyyxx

0346 yx

1,2and1,1 ofbisector OR

0,21

211,

221M

izizge 21..

2222 1211 yxyx12441212 2222 yyxxyyxx

0346 yx

1,2and1,1 ofbisector OR

0,21

211,

221M

izizge 21..

32

2111

m

2222 1211 yxyx12441212 2222 yyxxyyxx

0346 yx

1,2and1,1 ofbisector OR

0,21

211,

221M

23 is slope required

izizge 21..

32

2111

m

2222 1211 yxyx12441212 2222 yyxxyyxx

0346 yx

1,2and1,1 ofbisector OR

0,21

211,

221M

23 is slope required

21

230 xy

izizge 21..

32

2111

m

2222 1211 yxyx12441212 2222 yyxxyyxx

0346 yx

1,2and1,1 ofbisector OR

0,21

211,

221M

23 is slope required

21

230 xy

izizge 21..

32

2111

m

03462332

yx

xy

izizii 42Sketch

izizii 42Sketch y

x-2

4

1

izizii 42Sketch y

x-2

4

1

izizii 42Sketch y

x-2

4

1

Rays

y

x

izizii 42Sketch y

x-2

4

1

Rays

y

x

zarg

izizii 42Sketch y

x-2

4

1

Rays

y

x

zarg

y

x

izizii 42Sketch y

x-2

4

1

Rays

y

x

zarg

y

x

zarg

4arg0 and 1 e.g.

zz

4arg0 and 1 e.g.

zz

y

x

1

1

-1

-1

1z

4arg0 and 1 e.g.

zz

y

x

1

1

-1

-1

1z

4

4arg

z

0arg z

4arg0 and 1 e.g.

zz

y

x

1

1

-1

-1

1z

4

4arg

z

0arg z

4arg0 and 1 e.g.

zz

y

x

1

1

-1

-1

1z

4

4arg

z

0arg z

Patel: Exercise 4M; 1ac, 2bd, 3, 4, 5bd, 6

Patel: Exercise 4N; 1a to j, 2ace, 3ace etc, 4ace

Cambridge: Exercise 1F; 1 to 5 ace etc, 6, 7 ac, 8