z = − 2 + 3 i z=-2+\sqrt{3}i z = − 2 + 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> i có ∣ z ∣ \left|z\right| ∣ z ∣ bằng

∣ z ∣ = 7 \left|z\right|=\sqrt{7} ∣ z ∣ = 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 5 \left|z\right|=\sqrt{5} ∣ z ∣ = 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 6 \left|z\right|=6 ∣ z ∣ = 6

∣ z ∣ = 3 \left|z\right|=3 ∣ z ∣ = 3

T ı ˋ m z ‾ Tìm\ \overline{z} T ı ˋ m z ,biết z = 1 − i 3 z=1-i\sqrt{3} z = 1 − i 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

z ‾ = i 3 + 1 \overline{z}=i\sqrt{3}+1 z = i 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 1

z ‾ = 1 + 3 i \overline{z}=1+3i z = 1 + 3 i

z = 1 + i 3 z=1+i\sqrt{3} z = 1 + i 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

I = ( 1 + i ) 2018 I=\left(1+i\right)^{2018} I = ( 1 + i ) 2 0 1 8 .Giá trị của I bằng

I = 2 1009 i I=2^{1009}i I = 2 1 0 0 9 i

I = 2 2018 I=2^{2018} I = 2 2 0 1 8

I = 2018 i I=2018i I = 2 0 1 8 i

I = 2 1008 I=2^{1008} I = 2 1 0 0 8

Cho số phức z = a + b i ( a , b ∈ R ) z=a+bi\left(a,b\in R\right) z = a + b i ( a , b ∈ R ) thỏa mãn ( 1 + i ) z + 2 z ‾ = 3 + 2 i . \left(1+i\right)z+2\overline{z}=3+2i. ( 1 + i ) z + 2 z = 3 + 2 i . Tính P = a + b P=a+b P = a + b

P = − 2 3 P=-\frac{2}{3} P = − 3 2

Tập hợp các điểm trong mặt phẳng phức biểu diễn các số phức z thỏa mãn ∣ z − 3 + 5 i ∣ = 4 \left|z-3+5i\right|=4 ∣ z − 3 + 5 i ∣ = 4 là một đường tròn.Tính chu vi C của đường tròn đó

C = 5 π C=\sqrt{5}\pi C = 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> π

Cho số phức z = 3 + 2 i z=3+2i z = 3 + 2 i .Tìm số phức w = 2 i − ( 3 − i ) z ‾ + 2 i z − 1 w=2i-\left(3-i\right)\overline{z}+2iz-1 w = 2 i − ( 3 − i ) z + 2 i z − 1

w = − 12 + 17 i w=-12+17i w = − 1 2 + 1 7 i

w = 21 − 13 i w=21-13i w = 2 1 − 1 3 i

24 − 23 i 24-23i 2 4 − 2 3 i

Cho số phức z thỏa mãn z − 1 z − i = i \frac{z-1}{z-i}=i z − i z − 1 = i .Môđun của số phức w = ( 2 − i ) z − 1 w=\left(2-i\right)z-1 w = ( 2 − i ) z − 1 là

∣ w ∣ = 5 \left|w\right|=\sqrt{5} ∣ w ∣ = 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ w ∣ = 3 \left|w\right|=3 ∣ w ∣ = 3

∣ w ∣ = 7 \left|w\right|=\sqrt{7} ∣ w ∣ = 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ w ∣ = 2 \left|w\right|=\sqrt{2} ∣ w ∣ = 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Điểm biểu diễn của số phức z = 1 2 − 3 i z=\frac{1}{2-3i} z = 2 − 3 i 1 là

C ( 2 13 ; 3 13 ) C\left(\frac{2}{13};\frac{3}{13}\right) C ( 1 3 2 ; 1 3 3 )

A ( 1 3 ; − 7 3 ) A\left(\frac{1}{3};\frac{-7}{3}\right) A ( 3 1 ; 3 − 7 )

B ( 3 ; − 2 ) B\left(3;-2\right) B ( 3 ; − 2 )

D ( 12 ; − 9 ) D\left(12;-9\right) D ( 1 2 ; − 9 )

Cho số phức z thỏa mãn ∣ z + 1 ∣ = ∣ z + 3 − 2 i ∣ \left|z+1\right|=\left|z+3-2i\right| ∣ z + 1 ∣ = ∣ z + 3 − 2 i ∣ .Biết tập hợp các điểm biểu diễn số phức z là một đường thẳng có phương trình là

x − y + 3 = 0 x-y+3=0 x − y + 3 = 0

− 2 x + y − 2 = 0 -2\ x+y-2=0 − 2 x + y − 2 = 0

x + y − 2 = 0 x+y-2=0 x + y − 2 = 0

x − 2 y − 3 = 0 x-2y-3=0 x − 2 y − 3 = 0

Trong các số phức z thỏa mãn ∣ z + 3 i ∣ = ∣ z + 2 − i ∣ \ \left|z+3i\right|=\left|z+2-i\right| ∣ z + 3 i ∣ = ∣ z + 2 − i ∣ ,tìm số phức z có môđun nhỏ nhất

z = 1 5 − 2 5 i z=\frac{1}{5}-\frac{2}{5}i z = 5 1 − 5 2 i

z = 1 − 2 i z=1-2i z = 1 − 2 i

z = − 1 5 + 2 5 i z=-\frac{1}{5}+\frac{2}{5}i z = − 5 1 + 5 2 i

z = − 1 + 2 i z=-1+2i z = − 1 + 2 i

Cho số phức z = 3 − 5 i z=3-5i z = 3 − 5 i .Gọi a = R e ( z ) ; b = I m ( z ) a=Re\left(z\right);b=Im\left(z\right) a = R e ( z ) ; b = I m ( z ) .Tính S = a + b S=a+b S = a + b

S = − 3 5 S=-\frac{3}{5} S = − 5 3

Cho số phức z = 1 + i z=1+i z = 1 + i .Tìm số phức liên hợp của w = z ‾ + 2 i z − 1 w=\frac{\overline{z}+2i}{z-1} w = z − 1 z + 2 i

w ‾ = 1 + i \overline{w}=1+i w = 1 + i

w ‾ = 2 − i \overline{w}=2-i w = 2 − i

w ‾ = 1 − 3 i \overline{w}=1-3i w = 1 − 3 i

w ‾ = 3 i \overline{w}=3i w = 3 i

Tìm các số thực x,y thỏa mãn: 2 x − 1 + ( 1 − 2 y ) i = 2 − x + ( 3 y + 2 ) i 2\ x-1+\left(1-2y\right)i=2-x+\left(3y+2\right)i 2 x − 1 + ( 1 − 2 y ) i = 2 − x + ( 3 y + 2 ) i

x = 1 ; y = − 1 5 x=1;y=-\frac{1}{5} x = 1 ; y = − 5 1

x = − 2 ; y = 3 x=-2;y=3 x = − 2 ; y = 3

x = 2 ; y = − 1 x=2;y=-1 x = 2 ; y = − 1

x = 1 3 ; y = 1 2 x=\frac{1}{3};y=\frac{1}{2} x = 3 1 ; y = 2 1

Số phức z = ( 1 + i ) ( 2 − i ) z=\left(1+i\right)\left(2-i\right) z = ( 1 + i ) ( 2 − i ) có điểm biểu diễn là

M ( 3 ; 1 ) M\left(3;1\right) M ( 3 ; 1 )

N ( − 2 ; 3 ) N\left(-2;3\right) N ( − 2 ; 3 )

P ( − 2 ; 1 ) P\left(-2;1\right) P ( − 2 ; 1 )

Q ( − 2 ; 5 ) Q\left(-2;5\right) Q ( − 2 ; 5 )

Cho số phức z thỏa mãn z ‾ 4 − 3 i + ( 2 − 3 i ) = 5 − 2 i \frac{\overline{z}}{4-3i}+\left(2-3i\right)=5-2i 4 − 3 i z + ( 2 − 3 i ) = 5 − 2 i .Môđun của số phức z bằng

∣ z ∣ = 5 10 \left|z\right|=5\sqrt{10} ∣ z ∣ = 5 1 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 10 2 \left|z\right|=10\sqrt{2} ∣ z ∣ = 1 0 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 10 \left|z\right|=\sqrt{10} ∣ z ∣ = 1 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

∣ z ∣ = 2 10 \left|z\right|=2\sqrt{10} ∣ z ∣ = 2 1 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Nếu điểm M(x;y) là điểm biểu diễn của số phức z trong mặt phẳng tọa độ Oxy thỏa mãn OM=4 thì

∣ z ∣ = 4 \left|z\right|=4 ∣ z ∣ = 4

∣ z ∣ = 16 \left|z\right|=16 ∣ z ∣ = 1 6

∣ z ∣ = 2 \left|z\right|=2 ∣ z ∣ = 2

∣ z ∣ = 1 4 \left|z\right|=\frac{1}{4} ∣ z ∣ = 4 1

Cho số phức z thỏa mãn ∣ z + 1 ∣ = 2 \left|z+1\right|=2 ∣ z + 1 ∣ = 2 .Biết rằng tập hợp các điểm biểu diễn các số phức w = ( 1 + i 8 ) z + i w=\left(1+i\sqrt{8}\right)z+i w = ( 1 + i 8 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ) z + i là một đường tròn.Bán kính r của đường tròn đó là

r = 5 r=\sqrt{5} r = 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

( 3 + x ) + ( 1 + y ) i = 1 + 3 i \left(3+x\right)+\left(1+y\right)i=1+3i ( 3 + x ) + ( 1 + y ) i = 1 + 3 i Bộ số thực (x;y) thỏa mãn đẳng thức trên là

( x ; y ) = ( − 2 ; 2 ) \left(x;y\right)=\left(-2;2\right) ( x ; y ) = ( − 2 ; 2 )

( x ; y ) = ( 1 ; 2 ) \left(x;y\right)=\left(1;2\right) ( x ; y ) = ( 1 ; 2 )

( x ; y ) = ( − 1 ; 3 ) \left(x;y\right)=\left(-1;3\right) ( x ; y ) = ( − 1 ; 3 )

( x ; y ) = ( 0 ; 2 ) \left(x;y\right)=\left(0;2\right) ( x ; y ) = ( 0 ; 2 )

Nghiệm của phương trình i z + 2 − i = 0 iz+2-i=0 i z + 2 − i = 0

z = 1 − 3 i z=1-3i z = 1 − 3 i

z = 3 − 2 i z=3-2i z = 3 − 2 i

Số phức liên hợp của số phức z = a − b i ( a , b ∈ R ) z=a-bi\ \left(a,b\in R\right) z = a − b i ( a , b ∈ R ) là

z ‾ = a + b i \overline{z}=a+bi z = a + b i

z ‾ = a − b i \overline{z}=a-bi z = a − b i

z ‾ = ( a + b ) i \overline{z}=\left(a+b\right)i z = ( a + b ) i

z ‾ = ( a − b ) i \overline{z}=\left(a-b\right)i z = ( a − b ) i

Phần thực của số phức z = ( 1 + i ) 10 + ( 1 − i ) 10 z=\left(1+i\right)^{10}+\left(1-i\right)^{10} z = ( 1 + i ) 1 0 + ( 1 − i ) 1 0 là

2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

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ÔN TẬP CHƯƠNG III( SỐ PHỨC )

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$P=-\frac{2}{3}$

$P=\frac{1}{2}$

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$I=\left(1+i\right)^{2018}$ .Giá trị của I bằng

Cho z thỏa mãn $\left(2+i\right)z+\frac{2\left(1+2i\right)}{1+i}=7+8i$ .Kí hiệu a,b lần lượt là phần thực và phần ảo của số phức $w=z+1+i$ .Tính $P=a^2+b^2$

Cho số phức $z=a+bi\left(a,b\in R\right)$ thỏa mãn $\left(1+i\right)z+2\overline{z}=3+2i.$ Tính $P=a+b$

Tập hợp các điểm trong mặt phẳng phức biểu diễn các số phức z thỏa mãn $\left|z-3+5i\right|=4$ là một đường tròn.Tính chu vi C của đường tròn đó

Cho số phức $z=3+2i$ .Tìm số phức $w=2i-\left(3-i\right)\overline{z}+2iz-1$

Cho số phức z thỏa mãn $\frac{z-1}{z-i}=i$ .Môđun của số phức $w=\left(2-i\right)z-1$ là

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Tıˋm z‾Tìm\ \overline{z}Tıˋm z ,biết z=1−i3z=1-i\sqrt{3}z=1−i3​

Phương trình nào dưới đây nhận 1+2i1+\sqrt{2}i1+2​i và 1−2i1-\sqrt{2}i1−2​i là nghiệm?

I=(1+i)2018I=\left(1+i\right)^{2018}I=(1+i)2018 .Giá trị của I bằng

Cho z thỏa mãn (2+i)z+2(1+2i)1+i=7+8i\left(2+i\right)z+\frac{2\left(1+2i\right)}{1+i}=7+8i(2+i)z+1+i2(1+2i)​=7+8i .Kí hiệu a,b lần lượt là phần thực và phần ảo của số phức w=z+1+iw=z+1+iw=z+1+i .Tính P=a2+b2P=a^2+b^2P=a2+b2

Cho số phức z=a+bi(a,b∈R)z=a+bi\left(a,b\in R\right)z=a+bi(a,b∈R) thỏa mãn (1+i)z+2z‾=3+2i.\left(1+i\right)z+2\overline{z}=3+2i.(1+i)z+2z=3+2i. Tính P=a+bP=a+bP=a+b

Tập hợp các điểm trong mặt phẳng phức biểu diễn các số phức z thỏa mãn ∣z−3+5i∣=4\left|z-3+5i\right|=4∣z−3+5i∣=4 là một đường tròn.Tính chu vi C của đường tròn đó

Cho số phức z=3+2iz=3+2iz=3+2i .Tìm số phức w=2i−(3−i)z‾+2iz−1w=2i-\left(3-i\right)\overline{z}+2iz-1w=2i−(3−i)z+2iz−1

Cho số phức z thỏa mãn z−1z−i=i\frac{z-1}{z-i}=iz−iz−1​=i .Môđun của số phức w=(2−i)z−1w=\left(2-i\right)z-1w=(2−i)z−1 là

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$z=-2+\sqrt{3}i$ có $\left|z\right|$ bằng

$Tìm\ \overline{z}$ ,biết $z=1-i\sqrt{3}$

Phương trình nào dưới đây nhận $1+\sqrt{2}i$ và $1-\sqrt{2}i$ là nghiệm?

$I=\left(1+i\right)^{2018}$ .Giá trị của I bằng

Cho z thỏa mãn $\left(2+i\right)z+\frac{2\left(1+2i\right)}{1+i}=7+8i$ .Kí hiệu a,b lần lượt là phần thực và phần ảo của số phức $w=z+1+i$ .Tính $P=a^2+b^2$

Cho số phức $z=a+bi\left(a,b\in R\right)$ thỏa mãn $\left(1+i\right)z+2\overline{z}=3+2i.$ Tính $P=a+b$

Tập hợp các điểm trong mặt phẳng phức biểu diễn các số phức z thỏa mãn $\left|z-3+5i\right|=4$ là một đường tròn.Tính chu vi C của đường tròn đó

Cho số phức $z=3+2i$ .Tìm số phức $w=2i-\left(3-i\right)\overline{z}+2iz-1$

Cho số phức z thỏa mãn $\frac{z-1}{z-i}=i$ .Môđun của số phức $w=\left(2-i\right)z-1$ là