x2 t01 10 locus & complex numbers 1
TRANSCRIPT
Locus and Complex Numbers
Locus and Complex NumbersCircles
Locus and Complex NumbersCircles
y
x
R
R
R
R
Locus and Complex NumbersCircles
y
x
R
R
R
R
Rz
Locus and Complex NumbersCircles
y
x
R
R
R
R
Rz
or2Rzz
Locus and Complex NumbersCircles
y
x
Ry
xR
R
R
Rz
or2Rzz
R
Locus and Complex NumbersCircles
y
x
Ry
xR
R
R
Rz
or2Rzz
R
Rz
Locus and Complex NumbersCircles
y
x
Ry
xR
R
R
Rz
or2Rzz
R
Rz
or 2Rzz
e.g. (i) Express these circles in terms of z
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
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;
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
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 ,
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
izz 23 c)
izz 23
2222 1299 yxyx
izz 23 c)
izz 23
2222 1299 yxyx124499 2222 yyxxyx
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 ,
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
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 ,
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
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
Exercise 4M; 1ac, 2bd, 3, 4,5bd, 6