Drawing an Argand diagram for complex numbers

[icystrike]

Homework Statement

I'm looking at the part that requires me to draw the argand diagram.

Homework Equations

The Attempt at a Solution

 

[Mentallic]

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.

 

[snshusat161]

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)

 

[snshusat161]

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 $$re^{i\theta}$$

 

[Mentallic]

You amuse me snshusat161

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)

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]

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.

saying LaTeX Code: \\theta=arg(z) is trivial since if you know what one means then you should know what the other means

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