Complex number roots, complex plane
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1.What figure complex roots of this equation create $$z^4+16z^2+100=0$$
2.What are the equations of straight lines that link vertexes of this figure
I don't know how to proceed
$z^2=x$ , $x^2+16x+100=0$ , $delta=-144=144i^2$ ,$sqrt{delta}=12i$ ,
$x_1^2=dfrac{ -16-12i}{4}=sqrt{-4-3i} ,:x_2^2=dfrac{ -16+12i}{4}=sqrt{-4+3i}$.
The second part of this task is to rotate 90 degrees said figure and find vertexes using a) complex numbers b) rotation matrix
complex-numbers
asked Nov 18 at 13:37
B. Czostek
294
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up vote
2
down vote
favorite
1.What figure complex roots of this equation create $$z^4+16z^2+100=0$$
2.What are the equations of straight lines that link vertexes of this figure
I don't know how to proceed
$z^2=x$ , $x^2+16x+100=0$ , $delta=-144=144i^2$ ,$sqrt{delta}=12i$ ,
$x_1^2=dfrac{ -16-12i}{4}=sqrt{-4-3i} ,:x_2^2=dfrac{ -16+12i}{4}=sqrt{-4+3i}$.
The second part of this task is to rotate 90 degrees said figure and find vertexes using a) complex numbers b) rotation matrix
complex-numbers
asked Nov 18 at 13:37
B. Czostek
294
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
1.What figure complex roots of this equation create $$z^4+16z^2+100=0$$
2.What are the equations of straight lines that link vertexes of this figure
I don't know how to proceed
$z^2=x$ , $x^2+16x+100=0$ , $delta=-144=144i^2$ ,$sqrt{delta}=12i$ ,
$x_1^2=dfrac{ -16-12i}{4}=sqrt{-4-3i} ,:x_2^2=dfrac{ -16+12i}{4}=sqrt{-4+3i}$.
The second part of this task is to rotate 90 degrees said figure and find vertexes using a) complex numbers b) rotation matrix
complex-numbers
asked Nov 18 at 13:37
B. Czostek
294
1.What figure complex roots of this equation create $$z^4+16z^2+100=0$$
2.What are the equations of straight lines that link vertexes of this figure
I don't know how to proceed
$z^2=x$ , $x^2+16x+100=0$ , $delta=-144=144i^2$ ,$sqrt{delta}=12i$ ,
$x_1^2=dfrac{ -16-12i}{4}=sqrt{-4-3i} ,:x_2^2=dfrac{ -16+12i}{4}=sqrt{-4+3i}$.
The second part of this task is to rotate 90 degrees said figure and find vertexes using a) complex numbers b) rotation matrix
complex-numbers
complex-numbers
asked Nov 18 at 13:37
B. Czostek
294
asked Nov 18 at 13:37
B. Czostek
294
asked Nov 18 at 13:37
B. Czostek
294
asked Nov 18 at 13:37
B. Czostek
294
asked Nov 18 at 13:37
B. Czostek
294
294
add a comment |
add a comment |
1 Answer
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$$x_1^2=-4-3i$$
Let $x_1=a+bi$ so $$-4-3i =(a+bi)^2=a^2-b^2+2abi$$
so $2ab =-3$ and $a^2-b^2=-4$. Now solve this system if $a,b$ are real...
answered Nov 18 at 15:02
greedoid
35.8k114590
I did and got these: $ frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i $
– B. Czostek
Nov 18 at 16:47
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
$$x_1^2=-4-3i$$
Let $x_1=a+bi$ so $$-4-3i =(a+bi)^2=a^2-b^2+2abi$$
so $2ab =-3$ and $a^2-b^2=-4$. Now solve this system if $a,b$ are real...
answered Nov 18 at 15:02
greedoid
35.8k114590
I did and got these: $ frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i $
– B. Czostek
Nov 18 at 16:47
add a comment |
up vote
0
down vote
$$x_1^2=-4-3i$$
Let $x_1=a+bi$ so $$-4-3i =(a+bi)^2=a^2-b^2+2abi$$
so $2ab =-3$ and $a^2-b^2=-4$. Now solve this system if $a,b$ are real...
answered Nov 18 at 15:02
greedoid
35.8k114590
I did and got these: $ frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i $
– B. Czostek
Nov 18 at 16:47
add a comment |
up vote
0
down vote
up vote
0
down vote
$$x_1^2=-4-3i$$
Let $x_1=a+bi$ so $$-4-3i =(a+bi)^2=a^2-b^2+2abi$$
so $2ab =-3$ and $a^2-b^2=-4$. Now solve this system if $a,b$ are real...
answered Nov 18 at 15:02
greedoid
35.8k114590
$$x_1^2=-4-3i$$
Let $x_1=a+bi$ so $$-4-3i =(a+bi)^2=a^2-b^2+2abi$$
so $2ab =-3$ and $a^2-b^2=-4$. Now solve this system if $a,b$ are real...
answered Nov 18 at 15:02
greedoid
35.8k114590
answered Nov 18 at 15:02
greedoid
35.8k114590
answered Nov 18 at 15:02
greedoid
35.8k114590
answered Nov 18 at 15:02
greedoid
35.8k114590
35.8k114590
I did and got these: $ frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i $
– B. Czostek
Nov 18 at 16:47
add a comment |
I did and got these: $ frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i $
– B. Czostek
Nov 18 at 16:47
I did and got these: $ frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i $
– B. Czostek
Nov 18 at 16:47
I did and got these: $ frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , frac {sqrt{2}}{2} + frac {3 sqrt{2}}{2}i , -frac {sqrt{2}}{2} - frac {3 sqrt{2}}{2}i $
– B. Czostek
Nov 18 at 16:47
add a comment |
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