Complex Numbers (Locus) (2 Viewers)

[mRym]

Hi, can someone please help me with the following question:

Graph r = theta where r is the distance from 0 and theta is any angle in [-pi < theta <= pi].

Thanks!

 

[Carrotsticks]

That is a somewhat confusing question.

"The distance of the point from 0 is between -pi and pi"

Since the distance cannot be negative, we revise the statement.

"The distance of the point from 0 is between 0 and pi"

It is a shaded circle of radius pi.

 

[braintic]

That is a somewhat confusing question.

"The distance of the point from 0 is between -pi and pi"

Since the distance cannot be negative, we revise the statement.

"The distance of the point from 0 is between 0 and pi"

It is a shaded circle of radius pi.

Isn't it a spiral?

 

[Carrotsticks]

Isn't it a spiral?

On second thought, I am quite sure my notion of the infinitely tight spiral (or more accurately infinitely many concentric circles) is correct.

It would be a spiral if Z=Rcis(theta), and we are sketching the locus of Z if r=theta. This way, we ensure rotation whilst 'lengthening' the modulus.

Take for example theta=pi/4.

So r=pi/4 since r = theta, meaning the distance of the point say Z from the origin is pi/4, making a circle. There is no mention that the point has to take on the same argument as theta.

 

[mRym]

Isn't it a spiral?

Actually yes you are correct.

I had thought of it as an 'infinitely tight' spiral, which made a shaded circle.

Thanks!
The answer has this :

But how do u know how to sketch it?

 

[braintic]

There is no mention that the point has to take on the same argument as theta.

But I'm sure that was the implication. I think its just a poorly worded question.

Thanks!
The answer has this :

But how do u know how to sketch it?

Isn't that the graph of r = | theta | ?

 

[mRym]

But I'm sure that was the implication. I think its just a poorly worded question.



Isn't that the graph of r = | theta | ?

when i put in wolfram "r = theta" i geet

but if i also restrict theta it gives me

 

[Carrotsticks]

That's because they understand R and theta to be Rcis(theta).

But the given question makes no mention of 'cis' or cos+isin.

R is the usual definition of R, which is distance from the origin.

But theta had no attached definitions as the argument. It is simply defined as a number that ranges from -pi to pi. We could have used 'x' for all we care.

The shape you got from Wolfram is the process of a spiral gone up to pi, then it 'rotates backwards' to satisfy the -pi, if that makes sense.

 

[mRym]

That's because they understand R and theta to be Rcis(theta).

But the given question makes no mention of 'cis' or cos+isin.

R is the usual definition of R, which is distance from the origin.

But theta had no attached definitions as the argument. It is simply defined as a number that ranges from -pi to pi. We could have used 'x' for all we care.

The shape you got from Wolfram is the process of a spiral gone up to pi, then it 'rotates backwards' to satisfy the -pi, if that makes sense.

Ahh okay, that makes sense.
Thanks