Mixing
$Amp(z)+Amp(w)=pi.;$ Find a relation between $;z;$ and $;w.$
$begingroup$
The question says:
Let $;z;$ and $;w;$ be two non-zero complex numbers such that $|z|=|w|$ and $amp(z)+amp(w)=pi,;$ then find a relation between $;z;$ and $;w.$
In the solution they turn $ amp(z)+amp(w)$ into $amp(Z)-amp(overline w);$ and equate it to $pi$. What was the need to do so ? I think I may be missing some concept.
The final answer is $;z+ overline w=0.$
complex-numbers
edited Jan 22 at 9:55
user376343
3,9234829
asked Jan 22 at 4:46
Hunter664Hunter664
113
$endgroup$
add a comment |
$begingroup$
The question says:
Let $;z;$ and $;w;$ be two non-zero complex numbers such that $|z|=|w|$ and $amp(z)+amp(w)=pi,;$ then find a relation between $;z;$ and $;w.$
In the solution they turn $ amp(z)+amp(w)$ into $amp(Z)-amp(overline w);$ and equate it to $pi$. What was the need to do so ? I think I may be missing some concept.
The final answer is $;z+ overline w=0.$
complex-numbers
edited Jan 22 at 9:55
user376343
3,9234829
asked Jan 22 at 4:46
Hunter664Hunter664
113
$endgroup$
1
$begingroup$
What is $amp$? Is it argument of the complex number?
$endgroup$
– user376343
Jan 22 at 9:52
add a comment |
$begingroup$
The question says:
Let $;z;$ and $;w;$ be two non-zero complex numbers such that $|z|=|w|$ and $amp(z)+amp(w)=pi,;$ then find a relation between $;z;$ and $;w.$
In the solution they turn $ amp(z)+amp(w)$ into $amp(Z)-amp(overline w);$ and equate it to $pi$. What was the need to do so ? I think I may be missing some concept.
The final answer is $;z+ overline w=0.$
complex-numbers
edited Jan 22 at 9:55
user376343
3,9234829
asked Jan 22 at 4:46
Hunter664Hunter664
113
$endgroup$
The question says:
Let $;z;$ and $;w;$ be two non-zero complex numbers such that $|z|=|w|$ and $amp(z)+amp(w)=pi,;$ then find a relation between $;z;$ and $;w.$
In the solution they turn $ amp(z)+amp(w)$ into $amp(Z)-amp(overline w);$ and equate it to $pi$. What was the need to do so ? I think I may be missing some concept.
The final answer is $;z+ overline w=0.$
complex-numbers
complex-numbers
edited Jan 22 at 9:55
user376343
3,9234829
asked Jan 22 at 4:46
Hunter664Hunter664
113
edited Jan 22 at 9:55
user376343
3,9234829
asked Jan 22 at 4:46
Hunter664Hunter664
113
edited Jan 22 at 9:55
user376343
3,9234829
edited Jan 22 at 9:55
user376343
3,9234829
edited Jan 22 at 9:55
user376343
3,9234829
3,9234829
asked Jan 22 at 4:46
Hunter664Hunter664
113
asked Jan 22 at 4:46
Hunter664Hunter664
113
asked Jan 22 at 4:46
Hunter664Hunter664
113
113
1
$begingroup$
What is $amp$? Is it argument of the complex number?
$endgroup$
– user376343
Jan 22 at 9:52
add a comment |
1
$begingroup$
What is $amp$? Is it argument of the complex number?
$endgroup$
– user376343
Jan 22 at 9:52
1
1
$begingroup$
What is $amp$? Is it argument of the complex number?
$endgroup$
– user376343
Jan 22 at 9:52
$begingroup$
What is $amp$? Is it argument of the complex number?
$endgroup$
– user376343
Jan 22 at 9:52
add a comment |
1 Answer
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$begingroup$
$$w=|w|e^{iangle w}=|z|e^{ipi-iangle z}=e^{ipi}|z|e^{-iangle z}=-overline z.$$
answered Jan 22 at 9:58
Yves DaoustYves Daoust
129k676227
$endgroup$
add a comment |
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$begingroup$
$$w=|w|e^{iangle w}=|z|e^{ipi-iangle z}=e^{ipi}|z|e^{-iangle z}=-overline z.$$
answered Jan 22 at 9:58
Yves DaoustYves Daoust
129k676227
$endgroup$
add a comment |
$begingroup$
$$w=|w|e^{iangle w}=|z|e^{ipi-iangle z}=e^{ipi}|z|e^{-iangle z}=-overline z.$$
answered Jan 22 at 9:58
Yves DaoustYves Daoust
129k676227
$endgroup$
add a comment |
$begingroup$
$$w=|w|e^{iangle w}=|z|e^{ipi-iangle z}=e^{ipi}|z|e^{-iangle z}=-overline z.$$
answered Jan 22 at 9:58
Yves DaoustYves Daoust
129k676227
$endgroup$
$$w=|w|e^{iangle w}=|z|e^{ipi-iangle z}=e^{ipi}|z|e^{-iangle z}=-overline z.$$
answered Jan 22 at 9:58
Yves DaoustYves Daoust
129k676227
answered Jan 22 at 9:58
Yves DaoustYves Daoust
129k676227
answered Jan 22 at 9:58
Yves DaoustYves Daoust
129k676227
answered Jan 22 at 9:58
Yves DaoustYves Daoust
129k676227
129k676227
add a comment |
add a comment |
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$begingroup$
What is $amp$? Is it argument of the complex number?
$endgroup$
– user376343
Jan 22 at 9:52