Find the complex numbers that satisfy the equation
up vote
0
down vote
favorite
I have
$$|z-3i|={sqrt{5}}, 0 < arg(z) le {frac{pi}{4}}$$
I found
$$x^2+(y-3)^2 = 5$$
Therefore, the circle with $y=3$ and radius ${sqrt{5}}$. But how do I use the fact about $arg(z)$?
complex-numbers
asked Nov 26 at 16:31
user3132457
856
add a comment |
up vote
0
down vote
favorite
I have
$$|z-3i|={sqrt{5}}, 0 < arg(z) le {frac{pi}{4}}$$
I found
$$x^2+(y-3)^2 = 5$$
Therefore, the circle with $y=3$ and radius ${sqrt{5}}$. But how do I use the fact about $arg(z)$?
complex-numbers
asked Nov 26 at 16:31
user3132457
856
Do you understand the relation between $arg(z)$ and angles?
– Lee Mosher
Nov 26 at 16:33
If $arg(z) in (0,frac pi 4]$ then (x,y) are in QI, and $yle x$
– Doug M
Nov 26 at 16:48
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have
$$|z-3i|={sqrt{5}}, 0 < arg(z) le {frac{pi}{4}}$$
I found
$$x^2+(y-3)^2 = 5$$
Therefore, the circle with $y=3$ and radius ${sqrt{5}}$. But how do I use the fact about $arg(z)$?
complex-numbers
asked Nov 26 at 16:31
user3132457
856
I have
$$|z-3i|={sqrt{5}}, 0 < arg(z) le {frac{pi}{4}}$$
I found
$$x^2+(y-3)^2 = 5$$
Therefore, the circle with $y=3$ and radius ${sqrt{5}}$. But how do I use the fact about $arg(z)$?
complex-numbers
complex-numbers
asked Nov 26 at 16:31
user3132457
856
asked Nov 26 at 16:31
user3132457
856
asked Nov 26 at 16:31
user3132457
856
asked Nov 26 at 16:31
user3132457
856
asked Nov 26 at 16:31
user3132457
856
856
Do you understand the relation between $arg(z)$ and angles?
– Lee Mosher
Nov 26 at 16:33
If $arg(z) in (0,frac pi 4]$ then (x,y) are in QI, and $yle x$
– Doug M
Nov 26 at 16:48
add a comment |
Do you understand the relation between $arg(z)$ and angles?
– Lee Mosher
Nov 26 at 16:33
If $arg(z) in (0,frac pi 4]$ then (x,y) are in QI, and $yle x$
– Doug M
Nov 26 at 16:48
Do you understand the relation between $arg(z)$ and angles?
– Lee Mosher
Nov 26 at 16:33
Do you understand the relation between $arg(z)$ and angles?
– Lee Mosher
Nov 26 at 16:33
If $arg(z) in (0,frac pi 4]$ then (x,y) are in QI, and $yle x$
– Doug M
Nov 26 at 16:48
If $arg(z) in (0,frac pi 4]$ then (x,y) are in QI, and $yle x$
– Doug M
Nov 26 at 16:48
add a comment |
2 Answers
2
active
oldest
votes
up vote
0
down vote
accepted
Hint:
take a picture of the circle and of the line $arg(z)=frac{pi}{4}$ (that is the bisector of the first quadrant in the Argand Plane). And note that this line intersect the circle in two points.
answered Nov 26 at 16:43
Emilio Novati
51.2k43472
add a comment |
up vote
0
down vote
The argument of a complex number gives the angle to the positive real axis. Can you use this for your problem?
answered Nov 26 at 16:35
Y. Forman
11.4k423
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
Hint:
take a picture of the circle and of the line $arg(z)=frac{pi}{4}$ (that is the bisector of the first quadrant in the Argand Plane). And note that this line intersect the circle in two points.
answered Nov 26 at 16:43
Emilio Novati
51.2k43472
add a comment |
up vote
0
down vote
accepted
Hint:
take a picture of the circle and of the line $arg(z)=frac{pi}{4}$ (that is the bisector of the first quadrant in the Argand Plane). And note that this line intersect the circle in two points.
answered Nov 26 at 16:43
Emilio Novati
51.2k43472
add a comment |
up vote
0
down vote
accepted
up vote
0
down vote
accepted
Hint:
take a picture of the circle and of the line $arg(z)=frac{pi}{4}$ (that is the bisector of the first quadrant in the Argand Plane). And note that this line intersect the circle in two points.
answered Nov 26 at 16:43
Emilio Novati
51.2k43472
Hint:
take a picture of the circle and of the line $arg(z)=frac{pi}{4}$ (that is the bisector of the first quadrant in the Argand Plane). And note that this line intersect the circle in two points.
answered Nov 26 at 16:43
Emilio Novati
51.2k43472
answered Nov 26 at 16:43
Emilio Novati
51.2k43472
answered Nov 26 at 16:43
Emilio Novati
51.2k43472
answered Nov 26 at 16:43
Emilio Novati
51.2k43472
51.2k43472
add a comment |
add a comment |
up vote
0
down vote
The argument of a complex number gives the angle to the positive real axis. Can you use this for your problem?
answered Nov 26 at 16:35
Y. Forman
11.4k423
add a comment |
up vote
0
down vote
The argument of a complex number gives the angle to the positive real axis. Can you use this for your problem?
answered Nov 26 at 16:35
Y. Forman
11.4k423
add a comment |
up vote
0
down vote
up vote
0
down vote
The argument of a complex number gives the angle to the positive real axis. Can you use this for your problem?
answered Nov 26 at 16:35
Y. Forman
11.4k423
The argument of a complex number gives the angle to the positive real axis. Can you use this for your problem?
answered Nov 26 at 16:35
Y. Forman
11.4k423
answered Nov 26 at 16:35
Y. Forman
11.4k423
answered Nov 26 at 16:35
Y. Forman
11.4k423
answered Nov 26 at 16:35
Y. Forman
11.4k423
11.4k423
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3014543%2ffind-the-complex-numbers-that-satisfy-the-equation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Do you understand the relation between $arg(z)$ and angles?
– Lee Mosher
Nov 26 at 16:33
If $arg(z) in (0,frac pi 4]$ then (x,y) are in QI, and $yle x$
– Doug M
Nov 26 at 16:48