Complex Number equation: $z+2barz= |barz+3|$
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Solve $z+2barz= |barz+3|$.
I'm new to complex numbers and need help solving this equation. Appreciate the assistance. Thanks.
**Edit: I've understood it now, i have to compare the real and imaginary parts. Thanks everyone, have a great day ahead!
complex-numbers
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up vote
0
down vote
favorite
Solve $z+2barz= |barz+3|$.
I'm new to complex numbers and need help solving this equation. Appreciate the assistance. Thanks.
**Edit: I've understood it now, i have to compare the real and imaginary parts. Thanks everyone, have a great day ahead!
complex-numbers
The question is no longer open.
â Paul Frost
Sep 1 at 0:08
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Solve $z+2barz= |barz+3|$.
I'm new to complex numbers and need help solving this equation. Appreciate the assistance. Thanks.
**Edit: I've understood it now, i have to compare the real and imaginary parts. Thanks everyone, have a great day ahead!
complex-numbers
Solve $z+2barz= |barz+3|$.
I'm new to complex numbers and need help solving this equation. Appreciate the assistance. Thanks.
**Edit: I've understood it now, i have to compare the real and imaginary parts. Thanks everyone, have a great day ahead!
complex-numbers
edited Aug 25 at 8:26
asked Aug 25 at 8:12
Nick
11
11
The question is no longer open.
â Paul Frost
Sep 1 at 0:08
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The question is no longer open.
â Paul Frost
Sep 1 at 0:08
The question is no longer open.
â Paul Frost
Sep 1 at 0:08
The question is no longer open.
â Paul Frost
Sep 1 at 0:08
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
0
down vote
HINT
Since
$$z+2bar z=|bar z+3|$$
and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve
$$3x=|x+3|$$
add a comment |Â
up vote
0
down vote
Let $z=x+iy$ then
$$(x+iy)+(2x-2iy)=|x-iy+3|$$
$$3x-iy=|(x+3)-iy|$$
shows
$$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
can you proceed?
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up vote
0
down vote
Note that $z+2overline z$ must be real, which is only possible if $z$ is real !
Then $$3x=|x+3|$$
and $x$ must be positive.
Finally,
$$3x=x+3.$$
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
HINT
Since
$$z+2bar z=|bar z+3|$$
and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve
$$3x=|x+3|$$
add a comment |Â
up vote
0
down vote
HINT
Since
$$z+2bar z=|bar z+3|$$
and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve
$$3x=|x+3|$$
add a comment |Â
up vote
0
down vote
up vote
0
down vote
HINT
Since
$$z+2bar z=|bar z+3|$$
and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve
$$3x=|x+3|$$
HINT
Since
$$z+2bar z=|bar z+3|$$
and $z+bar z=2Re(z)$ we have that $z=bar z=x$ is real then it reduces to solve
$$3x=|x+3|$$
answered Aug 25 at 8:17
gimusi
70k73786
70k73786
add a comment |Â
add a comment |Â
up vote
0
down vote
Let $z=x+iy$ then
$$(x+iy)+(2x-2iy)=|x-iy+3|$$
$$3x-iy=|(x+3)-iy|$$
shows
$$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
can you proceed?
add a comment |Â
up vote
0
down vote
Let $z=x+iy$ then
$$(x+iy)+(2x-2iy)=|x-iy+3|$$
$$3x-iy=|(x+3)-iy|$$
shows
$$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
can you proceed?
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Let $z=x+iy$ then
$$(x+iy)+(2x-2iy)=|x-iy+3|$$
$$3x-iy=|(x+3)-iy|$$
shows
$$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
can you proceed?
Let $z=x+iy$ then
$$(x+iy)+(2x-2iy)=|x-iy+3|$$
$$3x-iy=|(x+3)-iy|$$
shows
$$3x=|(x+3)-iy|~~~~~textand~~~~~-iy=0$$
can you proceed?
answered Aug 25 at 8:17
Nosrati
21.4k41746
21.4k41746
add a comment |Â
add a comment |Â
up vote
0
down vote
Note that $z+2overline z$ must be real, which is only possible if $z$ is real !
Then $$3x=|x+3|$$
and $x$ must be positive.
Finally,
$$3x=x+3.$$
add a comment |Â
up vote
0
down vote
Note that $z+2overline z$ must be real, which is only possible if $z$ is real !
Then $$3x=|x+3|$$
and $x$ must be positive.
Finally,
$$3x=x+3.$$
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Note that $z+2overline z$ must be real, which is only possible if $z$ is real !
Then $$3x=|x+3|$$
and $x$ must be positive.
Finally,
$$3x=x+3.$$
Note that $z+2overline z$ must be real, which is only possible if $z$ is real !
Then $$3x=|x+3|$$
and $x$ must be positive.
Finally,
$$3x=x+3.$$
answered Aug 25 at 8:22
Yves Daoust
113k665207
113k665207
add a comment |Â
add a comment |Â
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The question is no longer open.
â Paul Frost
Sep 1 at 0:08