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{"id":22676,"date":"2018-03-20T15:22:45","date_gmt":"2018-03-20T08:22:45","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=22676"},"modified":"2018-03-21T16:21:09","modified_gmt":"2018-03-21T09:21:09","slug":"dai-so-chuong-4-cau-hoi-va-bai-tap-on-chuong-4","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/dai-so-chuong-4-cau-hoi-va-bai-tap-on-chuong-4\/","title":{"rendered":"\u0110\u1ea1i s\u1ed1 – Ch\u01b0\u01a1ng 4 – C\u00e2u h\u1ecfi v\u00e0 b\u00e0i t\u1eadp \u00f4n ch\u01b0\u01a1ng 4"},"content":{"rendered":"

B\u00e0i 37 (trang 208 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

T\u00ecm ph\u1ea7n th\u1ef1c v\u00e0 ph\u1ea7n \u1ea3o c\u1ee7a m\u1ed7i s\u1ed1 ph\u1ee9c sau:<\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

a) Ta c\u00f3: (2-3i)3<\/sup>=8-36i-54+27i=-46-9i c\u00f3 ph\u1ea7n th\u1ef1c l\u00e0 -46 v\u00e0 ph\u1ea7n \u1ea3n l\u00e0 -9<\/p>\n

b) Ta c\u00f3 s\u1ed1<\/p>\n

\"\"<\/p>\n

c) Ta c\u00f3: (x+iy)2<\/sup>-2(x+iy)+5=(x2<\/sup>-y2<\/sup>-2x+5)+(2xy-2y)i c\u00f3 ph\u1ea7n th\u1ee9c l\u00e0: (x2<\/sup>-y2<\/sup>-2x+5), c\u00f3 ph\u1ea7n \u1ea3o l\u00e0: (2xy-2y).<\/p>\n

\u0110\u1ec3 z l\u00e0 s\u1ed1 th\u1ef1c th\u00ec: (2xy-2y)=0 <=> y = 0 ho\u1eb7c x = 1.<\/p>\n

B\u00e0i 38 (trang 209 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

Ch\u1ee9ng minh r\u1eb1ng n\u1ebfu<\/p>\n

\"\"<\/p>\n

l\u00e0 s\u1ed1 th\u1ef1c (gi\u1ea3 s\u1eed 1 zw \u2260 0<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

Gi\u1ea3 s\u1eed z=z+bi,w=a’+b’i v\u1edbi a2<\/sup>+b2<\/sup>=a’2<\/sup>+b’2<\/sup>=1 v\u00e0 1+zw \u2260 0<\/p>\n

V\u00ec |z| = 1 n\u00ean z.z\u2212<\/i>=1<\/p>\n

Khi \u0111\u00f3, ta c\u00f3:<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

X\u00e9t ph\u1ea7n \u1ea3o \u1edf tr\u00ean t\u1eed s\u1ed1 ta c\u00f3: (b+b’ )(1+aa’-bb’ )-(a+a’ )(a’ b+ab’ )<\/p>\n

=b+baa’-b2<\/sup>b’+b’+b’ aa’-bb’2<\/sup>-aa’ b-a2<\/sup>\u00a0b’-a’2<\/sup>\u00a0b-a’ab’<\/p>\n

=b+b’-b’ (a2<\/sup>+b2<\/sup>\u00a0)-b(b’2<\/sup>+a’2<\/sup>\u00a0)=b+b’-b’-b=0<\/p>\n

\"\"<\/p>\n

B\u00e0i 39 (trang 209 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

Gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

a) \u0110\u1eb7t z+3-i=t, ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: t2<\/sup>-6t+13=0<\/p>\n

C\u00f3 \u03b4’=-4=(2i)2<\/sup>=>t1<\/sub>=3+2i;t2<\/sub>=3-2i<\/p>\n

V\u1edbi t1<\/sub>=3+2i=>z+3-i=3+2i=>z=3i<\/p>\n

V\u1edbi t2<\/sub>=3-2i=>z+3-i=3-2i=>z=-i<\/p>\n

V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 2 nghi\u1ec7m l\u00e0: 3i; -i<\/p>\n

\"\"<\/p>\n

ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: t2<\/sup>-3t-4=0<\/p>\n

=> t1<\/sub>=-1;t2<\/sub>=4<\/p>\n

\"\"<\/p>\n

V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m l\u00e0:<\/p>\n

\"\"<\/p>\n

c) (z2<\/sup>+1)2<\/sup>+(z+3)2<\/sup>=0<\/p>\n

<> (z2<\/sup>+1)2<\/sup>=-(z+3)2<\/sup>\u00a0<> (z2<\/sup>+1)2<\/sup>=[(z+3)i]2<\/sup><\/p>\n

\"\"<\/p>\n

V\u1eady ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 4 nghi\u1ec7m l\u00e0:<\/p>\n

\"\"<\/p>\n

B\u00e0i 40 (trang 209 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

Gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

a) \u0110\u1eb7t z+3-i=t, ta c\u00f3 Ph\u01b0\u01a1ng tr\u00ecnh: t2<\/sup>-6t+13=0<\/p>\n

C\u00f3 \u0394’=-4=(2i)2<\/sup>=>t1<\/sub>=3+2i;t2<\/sub>=3-2i<\/p>\n

V\u1edbi t1<\/sub>=3+2i=>z+3-i=3+2i=>z=3i<\/p>\n

V\u1edbi t2<\/sub>=3-2i=>z+3-i=3-2i=>z=-i<\/p>\n

V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 2 nghi\u1ec7m l\u00e0: 3i; -i<\/p>\n

b) \u0110\u1eb7t (iz+3)\/(z-2i)=t, ta c\u00f3 Ph\u01b0\u01a1ng tr\u00ecnh: t2<\/sup>-3t-4=0<\/p>\n

t1<\/sub>=-1;t2<\/sub>=4<\/p>\n

\"\"<\/p>\n

V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m l\u00e0:<\/p>\n

\"\"<\/p>\n

c) (z2<\/sup>+1)2<\/sup>+(z+3)2<\/sup>=0<\/p>\n

<=> (z2<\/sup>+1)2<\/sup>=-(z+3)2<\/sup>\u00a0<=> (z2<\/sup>+1)2<\/sup>=[(z+3)i]2<\/sup><\/p>\n

\"\"<\/p>\n

V\u1eady ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho c\u00f3 4 nghi\u1ec7m l\u00e0:<\/p>\n

\"\"<\/p>\n

B\u00e0i 41 (trang 209 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

Cho z=(\u221a6+\u221a2)+i(\u221a6-\u221a2)<\/p>\n

a) Vi\u1ebft z2<\/sup>\u00a0d\u01b0\u1edbi d\u1ea1ng \u0111\u1ea1i s\u1ed1 v\u00e0 l\u01b0\u1ee3ng gi\u00e1c.<\/p>\n

b) T\u1eeb c\u00e2u a h\u00e3y suy ra d\u1ea1ng l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a z.<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

a) Ta c\u00f3 z2<\/sup>=(\u221a6+\u221a2)2<\/sup>+(\u221a6-\u221a2)2<\/sup>+2i(\u221a6+\u221a2)(\u221a6-\u221a2)=8 \u221a3+8i<\/p>\n

M\u1eb7t kh\u00e1c:<\/p>\n

\"\"<\/p>\n

b) Ta c\u00f3 z l\u00e0 m\u1ed9t c\u0103n b\u1eadc hai c\u1ee7a z2<\/sup>\u00a0n\u00ean<\/p>\n

\"\"<\/p>\n

B\u00e0i 42 (trang 209 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

a) B\u1eb1ng c\u00e1ch bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc c\u00e1c s\u1ed1 ph\u1ee9c 2+i;3+i h\u00e3y ch\u1ee9ng minh r\u1eb1ng n\u1ebfu<\/p>\n

\"\"<\/p>\n

b) B\u1eb1ng c\u00e1ch bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc c\u00e1c s\u1ed1 ph\u1ee9c 2+i;5+i;8+i h\u00e3y ch\u1ee9ng minh r\u1eb1ng n\u1ebfu<\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

a) S\u1ed1 z = 2 + I c\u00f3 m\u1ed9t acgumen l\u00e0 a v\u1edbi tana = 1\/2;<\/p>\n

S\u1ed1 z\u2019 = 3 +I c\u00f3 s\u1ed1 acgumen l\u00e0 b v\u1edbi tanb=1\/3<\/p>\n

\"\"<\/p>\n

b) S\u1ed1 z1<\/sub>=2+i c\u00f3 acgumen l\u00e0 a v\u1edbi tana = 1\/2<\/p>\n

z2<\/sub>=5+i c\u00f3 m\u1ed9t acgumen l\u00e0 b v\u1edbi tanb = 1\/5<\/p>\n

z3<\/sub>=8+i c\u00f3 m\u1ed9t acgumen l\u00e0 c v\u1edbi tanc = 1\/8<\/p>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

B\u00e0i 37 (trang 208 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao): T\u00ecm ph\u1ea7n th\u1ef1c v\u00e0 ph\u1ea7n \u1ea3o c\u1ee7a m\u1ed7i s\u1ed1 ph\u1ee9c sau: L\u1eddi gi\u1ea3i: a) Ta c\u00f3: (2-3i)3=8-36i-54+27i=-46-9i c\u00f3 ph\u1ea7n th\u1ef1c l\u00e0 -46 v\u00e0 ph\u1ea7n \u1ea3n l\u00e0 -9 b) Ta c\u00f3 s\u1ed1 c) Ta c\u00f3: (x+iy)2-2(x+iy)+5=(x2-y2-2x+5)+(2xy-2y)i c\u00f3 ph\u1ea7n th\u1ee9c l\u00e0: (x2-y2-2x+5), c\u00f3 ph\u1ea7n \u1ea3o l\u00e0: (2xy-2y). […]<\/p>\n","protected":false},"author":3,"featured_media":22680,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1302],"tags":[1392,1393],"yoast_head":"\n\u0110\u1ea1i s\u1ed1 - Ch\u01b0\u01a1ng 4 - C\u00e2u h\u1ecfi v\u00e0 b\u00e0i t\u1eadp \u00f4n ch\u01b0\u01a1ng 4<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/dai-so-chuong-4-cau-hoi-va-bai-tap-on-chuong-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0110\u1ea1i s\u1ed1 - Ch\u01b0\u01a1ng 4 - C\u00e2u h\u1ecfi v\u00e0 b\u00e0i t\u1eadp \u00f4n ch\u01b0\u01a1ng 4\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 37 (trang 208 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao): T\u00ecm ph\u1ea7n th\u1ef1c v\u00e0 ph\u1ea7n \u1ea3o c\u1ee7a m\u1ed7i s\u1ed1 ph\u1ee9c sau: L\u1eddi gi\u1ea3i: a) Ta c\u00f3: (2-3i)3=8-36i-54+27i=-46-9i c\u00f3 ph\u1ea7n th\u1ef1c l\u00e0 -46 v\u00e0 ph\u1ea7n \u1ea3n l\u00e0 -9 b) Ta c\u00f3 s\u1ed1 c) Ta c\u00f3: (x+iy)2-2(x+iy)+5=(x2-y2-2x+5)+(2xy-2y)i c\u00f3 ph\u1ea7n th\u1ee9c l\u00e0: (x2-y2-2x+5), c\u00f3 ph\u1ea7n \u1ea3o l\u00e0: (2xy-2y). 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