- #1
Drawing an Argand Diagram: 2 Homework Statement
Click For Summary
SUMMARY
The discussion focuses on drawing an Argand diagram, specifically for complex numbers expressed in exponential and polar forms. Participants emphasize the importance of understanding the relationship between the rectangular form \( z = x + iy \) and its polar representation \( z = r(\cos\theta + i\sin\theta) \), where \( r = \sqrt{x^2 + y^2} \) and \( \theta = \arg(z) \). The conversation highlights the need for confidence in solving complex number problems and suggests that visualizing these concepts through diagrams can enhance comprehension.
PREREQUISITES- Understanding of complex numbers and their representations
- Familiarity with polar coordinates and trigonometric functions
- Knowledge of exponential form of complex numbers
- Basic skills in LaTeX for mathematical expressions
- Research how to construct Argand diagrams for various complex numbers
- Learn about the relationship between polar and rectangular forms of complex numbers
- Explore the use of LaTeX for formatting mathematical equations
- Study the properties of complex numbers in different mathematical contexts
Students studying complex numbers, mathematics educators, and anyone looking to improve their understanding of Argand diagrams and complex number representations.
- #2
Mentallic
Homework Helper
- 3,802
- 95
I'm at a loss here at what you're really asking. Do you need confirmation? In that case, your working is correct.
You seem to know how to solve complex numbers quite proficiently, and you yourself know this too. Confidence in your own abilities is a quality that anyone wanting to do well in an exam needs to have grasped. At these levels in mathematics, students are barely given enough time to be able to go back and check all their work thoroughly, and if you have an answer but can't quite move onto the next because of some slight irritating feeling that you might have made a small mistake, this will be worse for your results in the end.
You seem to know how to solve complex numbers quite proficiently, and you yourself know this too. Confidence in your own abilities is a quality that anyone wanting to do well in an exam needs to have grasped. At these levels in mathematics, students are barely given enough time to be able to go back and check all their work thoroughly, and if you have an answer but can't quite move onto the next because of some slight irritating feeling that you might have made a small mistake, this will be worse for your results in the end.
- #3
snshusat161
- 213
- 1
First Part: Express complex number in exponential form.
do you know what do you mean by exponential form.
Suppose z is any complex number. And if z = x + iy
then in polar form it will be written as
z = r (cos\theta + i sin\theta
where r = \sqrt{x^2 + y^2} and \theta = arg(z)
do you know what do you mean by exponential form.
Suppose z is any complex number. And if z = x + iy
then in polar form it will be written as
z = r (cos\theta + i sin\theta
where r = \sqrt{x^2 + y^2} and \theta = arg(z)
- #4
snshusat161
- 213
- 1
Now to solve your problem you have to know at which angle cos\theta has a value of -1/2 and sin\theta has a value of \frac{-\sqrt{3}}{2}. I'll not tell you unless you try something for it. If you can't find it after some try then post it here. I'll give you the angle.
And r can be easily calculated by you.
Now in exponential form you have to write it as re^{i\theta}
And r can be easily calculated by you.
Now in exponential form you have to write it as re^{i\theta}
- #5
Mentallic
Homework Helper
- 3,802
- 95
You amuse me snshusat161 
Stating what r is in terms of x and y is a good hint, but saying \theta=arg(z) is trivial since if you know what one means then you should know what the other means. You could just as well have said r=|z|
\theta=tan^{-1}\left(\frac{y}{x}\right)+(2k+1)\pi for all integers k, would have been much better.
Oh and the OP has already solved the problem, which is why I said what I said in post #2.
snshusat161, you've done it again
snshusat161 said:
Stating what r is in terms of x and y is a good hint, but saying \theta=arg(z) is trivial since if you know what one means then you should know what the other means. You could just as well have said r=|z|
\theta=tan^{-1}\left(\frac{y}{x}\right)+(2k+1)\pi for all integers k, would have been much better.
Oh and the OP has already solved the problem, which is why I said what I said in post #2.
snshusat161, you've done it again
- #6
snshusat161
- 213
- 1
I'm new here and don't have the habit to read another person's posts here. I only read the problem and try to give a little concept about it.
it's correct but actually I don't make anybody understand using formula rather I want to make them understand using diagram so that he can easily understand. I was searching how to draw diagram here but can't find anything so I've to stop.
And yeah, I've done it again and you are again the one to prompt me
it's correct but actually I don't make anybody understand using formula rather I want to make them understand using diagram so that he can easily understand. I was searching how to draw diagram here but can't find anything so I've to stop.
And yeah, I've done it again and you are again the one to prompt me
Similar threads
- · Replies 2 ·
- · Replies 3 ·
- · Replies 5 ·
- · Replies 2 ·
- · Replies 2 ·
- · Replies 2 ·
- · Replies 6 ·