Trắc nghiệm Phép chia số phức Toán Lớp 12

A. 0 và 1

B. 1 và 0

C. -1 và 0

D. 0 và -1

A. \(\begin{array}{l} z=-2+2 i . \end{array}\)

B. \( z=2-2 i .\)

C. \(z=2+2 i\)

D. \(z=-2-2 i \text { . }\)

A. 1

B. 2

C. 3

D. 4

A. \(\begin{array}{llll} 2^{2016} \end{array}\)

B. \(2^{3024}\)

C. \(2^{4032} \)

D. \( 2^{6048}\)

A. \(z=1-i\)

B. \(z=1+i\)

C. \(z=-1-i\)

D. \(z=1-2i\)

A. \(-2^{1009}-2^{1009} i . \)

B. \(2^{1009}+2^{1009} i . \)

C. \(-2^{2019}-2^{2019} i .\)

D. \(2^{2019}+2^{2019} i\)

A. \(\begin{array}{l} z=0, z=-\frac{1}{2}+\frac{1}{2} i, z=-\frac{1}{2}-\frac{1}{2} i \end{array}\)

B. \(z=0, z=-\frac{1}{2}+\frac{1}{2} i, z=\frac{1}{2}-\frac{1}{2} i \)

C. \(z=0, z=-1-\frac{1}{2} i, z=-1+\frac{1}{2} i \)

D. \(z=0, z=-\frac{1}{4}+\frac{1}{4} i, z=-\frac{1}{4}-\frac{1}{4} i\)

A. 0

B. \(2 \sqrt{2}\)

C. \(4 \sqrt{2}\)

D. \(6 \sqrt{2}\)

A. 1

B. 2

C. 3

D. 4

A. \(-26-170 i . \)

B. \(-26+170 i . \)

C. \(26-170 i\)

D. \(26+170 i\)

A. \(88-3 i\)

B. \(125+5 i\)

C. \(15-27 i\)

D. \(1-3 i\)

A. \(\begin{array}{l} (1+i)^{2016}=2^{1008} . \end{array}\)

B. \(\left|\frac{(1+i)^{2016}}{2^{1007}}-i\right|=\sqrt{5} \text { . }\)

C. \(\left|(1+i)^{2016}-2^{1008} i\right|=2^{1008} .\)

D. \((1+i)^{2016}=(1-i)^{2016} \text { . }\)

A. 0

B. 1

C. 2

D. 3

A. \(\sqrt{17}\) hoặc 5

B. \(\sqrt{17}\) hoặc -5

C. \(-\sqrt{17}\) hoặc 5

D. \(-\sqrt{17}\) hoặc -5

A. 4

B. 1

C. 2

D. 3

A. -1

B. 1

C. -2

D. 2

A. \(\frac{\sqrt{2}}{3}\)

B. \(\sqrt2\)

C. \(\frac{\sqrt{2}}{4}\)

D. \(\frac{\sqrt{3}}{4}\)

A. \(z=-2+i .\)

B. \(z=-2-i .\)

C. \(z=2+i .\)

D. \( z=2-i\)

A. 2

B. -2

C. 4

D. -4

A. \(\begin{array}{ll} (x ; y)=(-3 ; 4) \end{array}\)

B. \((x ; y)=(3 ; 4) . \)

C. \((x ; y)=(3 ;-4) . \)

D. \((x ; y)=(-3 ;-4) .\)

A. \(\begin{array}{l} \frac{1}{2} ; \frac{-\sqrt{3}}{2} \end{array}\)

B. \(\frac{1}{2} ;-\frac{\sqrt{3}}{2} i \text { . }\)

C. \(\frac{-1}{2} ;-\frac{\sqrt{3}}{2} . \)

D. \(-\frac{1}{2} ;-\frac{\sqrt{3}}{2} i\)

A. \(\left\{\begin{array} { l } { x = 0 } \\ { y = 0 } \end{array} . \right.\)

B. \(\left\{\begin{array} { l } { x = - \frac { 1 } { 7 } } \\ { y = - \frac { 4 } { 7 } } \end{array} .\right.\)

C. \( \left\{\begin{array} { c } { x = \frac { 4 } { 7 } } \\ { y = \frac { 1 } { 7 } } \end{array} .\right.\)

D. \(\left\{\begin{array}{c} x=-\frac{4}{7} \\ y=\frac{1}{7} \end{array} .\right.\)

A. \(z.\bar{z}=-|z|\)

B. \(\bar{z}=\frac{-1}{2}+\frac{\sqrt{3}}{2} i\)

C. \(|z|=\frac{\sqrt{2}}{2} i\)

D. \(|z|=1\)

A. \(\frac{z_{1}}{z_{2}}=1\)

B. \(z_{1}-z_{2}=0 . \)

C. \(z_{1} \cdot z_{2}=3-4 i .\)

D. \(\left|z_{1}\right|=-\left|z_{2}\right|\)

A. \(\begin{array}{l} \left|z_{1}\right|=5 \end{array}\)

B. \(\left|z_{1}\right|=\left|z_{2}\right| \text { . }\)

C. \(\left|z_{2}\right|=-5 .\)

D. \(z_{1}+z_{2}=1 \)

A. \(\frac{w}{z}=1\)

B. \(|z \cdot w|=|z| \cdot|w|=5\)

C. \(\left|\frac{z}{w}\right|=\frac{|z|}{|w|}=1\)

D. \({z \cdot w}=\bar{z} \cdot \bar{w}=4+3 i\)

A. \(\displaystyle   {{16} \over {17}}+ {{13} \over {17}}i.\)

B. \(\displaystyle   {{15} \over {17}} - {{13} \over {17}}i.\)

C. \(\displaystyle   {{16} \over {17}} - {{13} \over {17}}i.\)

D. \(\displaystyle   {{15} \over {17}} + {{13} \over {17}}i.\)

A. 3i - 2

B. - 3i - 2

C. - 3i + 2

D. 3i + 2

A. \(\displaystyle   {1 \over 2} - {{\sqrt 3 } \over 2}i\)

B. \(\displaystyle   {1 \over 2} + {{\sqrt 3 } \over 2}i\)

C. \(\displaystyle   {1 \over 2} + {{\sqrt 2 } \over 2}i\)

D. \(\displaystyle   {1 \over 2} - {{\sqrt 2 } \over 2}i\)

A. \(\displaystyle   {2 \over {13}} + {3 \over {13}}i\)

B. \(\displaystyle   {2 \over {13}} - {3 \over {13}}i\)

C. \(\displaystyle   {1 \over {13}} + {3 \over {13}}i\)

D. \(\displaystyle   {1 \over {13}} - {3 \over {13}}i\)

A. \(z \in \mathbb{R} \Leftrightarrow z = \overline z \)

B. \(z\) thuần ảo \( \Leftrightarrow z + \overline z  = 0\)

C. \(\dfrac{z}{{\overline z }} - \dfrac{{\overline z }}{z} \in \mathbb{R}\left( {z \ne 0} \right)\)

D. \({z^3} + {\left( {\overline z } \right)^3} \in \mathbb{R}\)

A. \(\dfrac{{{{\left( {1 + i} \right)}^5}}}{{{{\left( {1 - i} \right)}^3}}}\)

B. \({\left( {1 + i} \right)^5} + {\left( {1 - i} \right)^5}\)

C. \(\dfrac{{1 + i}}{{1 - i}} + \dfrac{{1 - i}}{{1 + i}}\)

D. \(\dfrac{{3 + 2i}}{{2 - i}} - \dfrac{{3 - 2i}}{{2 + i}}\)

A. \(\dfrac{{2 + i\sqrt 2 }}{{1 - i\sqrt 2 }} + \dfrac{{1 + i\sqrt 2 }}{{2 - i\sqrt 2 }}\)

B. \(\left( {2 + 3i} \right)\left( {3 - i} \right) + \left( {2 - 3i} \right)\left( {3 + i} \right)\)

C. \(\dfrac{{\left( {1 + i} \right)\left( {2 + i} \right)}}{{2 - i}} + \dfrac{{\left( {1 + i} \right)\left( {2 - i} \right)}}{{2 + i}}\)

D. \({\left( {2 + i\sqrt 3 } \right)^2} - {\left( {2 - i\sqrt 3 } \right)^2}\)

A. \( x=  2 - \dfrac{7}{2}i\)

B. \( x=  - 2 - \dfrac{7}{2}i\)

C. \( x=  - 2 + \dfrac{7}{2}i\)

D. \( x=  2 + \dfrac{7}{2}i\)

A. \(x= \dfrac{7}{5} - \dfrac{4}{5}i\)

B. \(x=- \dfrac{7}{5} - \dfrac{4}{5}i\)

C. \(x=- \dfrac{7}{5} + \dfrac{4}{5}i\)

D. \(x= \dfrac{7}{5} + \dfrac{4}{5}i\)

A. a = 0

B. b = 0

C. a = b

D. a = b hoặc a = -b

A. a = 0

B. b = 0

C. a = b

D. ab = 0

A. \(\dfrac{1}{z} \in \mathbb{R} \Leftrightarrow z \in \mathbb{R}\)

B. \(\dfrac{1}{z}\) là thuần ảo \( \Leftrightarrow z\) là thuần ảo

C. \(\dfrac{1}{z} = \overline z  \Leftrightarrow \left| z \right| = 1\)

D. \(\left| {\dfrac{1}{z}} \right| = \left| z \right| \Leftrightarrow z \in \mathbb{R}\)

A. z = - 4 + 3i

B. z = - 4 - 3i

C. z = 4 + 3i

D. z = 4 - 3i

A. z = 3 + i

B. z = 3 - i

C. z = 5 - i

D. z = 5 + i

A. \(  \dfrac{7}{{121}} + \dfrac{{6\sqrt 2 }}{{121}}i\)

B. \(  \dfrac{7}{{121}} - \dfrac{{6\sqrt 2 }}{{121}}i\)

C. \(-  \dfrac{7}{{121}} - \dfrac{{6\sqrt 2 }}{{121}}i\)

D. \( - \dfrac{7}{{121}} + \dfrac{{6\sqrt 2 }}{{121}}i\)

A. \(  \dfrac{{3 - 2\sqrt 5 }}{6} + \dfrac{{3\sqrt 5  + 2}}{6}i\)

B. \(  \dfrac{{3 - 2\sqrt 5 }}{6} - \dfrac{{3\sqrt 5  + 2}}{6}i\)

C. \(  \dfrac{{3 - 2\sqrt 5 }}{6} - \dfrac{{3\sqrt 5  - 2}}{6}i\)

D. \(  \dfrac{{3 + 2\sqrt 5 }}{6} - \dfrac{{3\sqrt 5  + 2}}{6}i\)

A. i

B. 1

C. -i

D. -1

A. \(\dfrac{{\sqrt 2 }}{5} + \dfrac{{\sqrt 3 }}{5}i\)

B. \(\dfrac{{\sqrt 2 }}{5} - \dfrac{{\sqrt 3 }}{5}i\)

C. \(-\dfrac{{\sqrt 2 }}{5} + \dfrac{{\sqrt 3 }}{5}i\)

D. \(-\dfrac{{\sqrt 2 }}{5}+ \dfrac{{\sqrt 3 }}{5}i\)

A. \(x=   \dfrac{{23}}{{89}} - \dfrac{{19}}{{89}}i\)

B. \(x=   \dfrac{{23}}{{89}} + \dfrac{{19}}{{89}}i\)

C. \(x=  - \dfrac{{23}}{{89}} - \dfrac{{19}}{{89}}i\)

D. \(x=  - \dfrac{{23}}{{89}} + \dfrac{{19}}{{89}}i\)

A. \(x= \dfrac{{23}}{{9}} + \dfrac{{14}}{{29}}i\)

B. \(x= \dfrac{{23}}{{9}} - \dfrac{{14}}{{29}}i\)

C. \(x= \dfrac{{23}}{{29}} + \dfrac{{14}}{{29}}i\)

D. \(x= \dfrac{{23}}{{29}} - \dfrac{{14}}{{29}}i\)

A. \(x= \dfrac{{42}}{{25}} - \dfrac{{19}}{{25}}i\)

B. \(x= \dfrac{{42}}{{2}} + \dfrac{{19}}{{25}}i\)

C. \(x= \dfrac{{42}}{{25}} + \dfrac{{19}}{{25}}i\)

D. \(x= \dfrac{{42}}{{2}} - \dfrac{{19}}{{25}}i\)

A. \(  \dfrac{{27}}{5} - \dfrac{9}{5}i\)

B. \(  \dfrac{{27}}{5} + \dfrac{9}{5}i\)

C. \(  \dfrac{{27}}{4} + \dfrac{9}{5}i\)

D. \(  \dfrac{{27}}{4} - \dfrac{9}{5}i\)

A. \( = \dfrac{{31}}{{13}} - \dfrac{{12}}{{13}}i\)

B. \( = \dfrac{{31}}{{13}} + \dfrac{{12}}{{13}}i\)

C. \( =- \dfrac{{31}}{{13}} - \dfrac{{12}}{{13}}i\)

D. \( = -\dfrac{{31}}{{13}} + \dfrac{{12}}{{13}}i\)

A. \(6 \sqrt{5}\)

B. \(4 \sqrt{5}\)

C. \(3 \sqrt{5}\)

D. \(5\sqrt{5}\)