Find the complex numbers that satisfy the equation
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
1336
add a comment |
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
1336
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 |
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
1336
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
1336
asked Nov 26 at 16:31
user3132457
1336
asked Nov 26 at 16:31
user3132457
1336
asked Nov 26 at 16:31
user3132457
1336
asked Nov 26 at 16:31
user3132457
1336
1336
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
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
51.5k43472
add a comment |
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
11.4k523
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
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
51.5k43472
add a comment |
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
51.5k43472
add a comment |
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
51.5k43472
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
51.5k43472
answered Nov 26 at 16:43
Emilio Novati
51.5k43472
answered Nov 26 at 16:43
Emilio Novati
51.5k43472
answered Nov 26 at 16:43
Emilio Novati
51.5k43472
51.5k43472
add a comment |
add a comment |
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
11.4k523
add a comment |
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
11.4k523
add a comment |
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
11.4k523
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
11.4k523
answered Nov 26 at 16:35
Y. Forman
11.4k523
answered Nov 26 at 16:35
Y. Forman
11.4k523
answered Nov 26 at 16:35
Y. Forman
11.4k523
11.4k523
add a comment |
add a comment |
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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