Plotting Points: How to Solve Equations with Complex Numbers

[DeathNinja]

Plot the set of points which satisy
Iz+1+jI=2

I2z+3I≤1

Im not sure about how to do this.

Sorry I am sure its very simple for you but can you just explain how to do one of them? I started maths later in life so I am not solid in mathematics.

Thanks a lot :-)

 

[DonAntonio]

Plot the set of points which satisy
Iz+1+jI=2

I2z+3I≤1

Im not sure about how to do this.

Sorry I am sure its very simple for you but can you just explain how to do one of them? I started maths later in life so I am not solid in mathematics.

Thanks a lot :-)

What is "I", "z", "j" ...??

DonAntonio

 

[DeathNinja]

What is "I", "z", "j" ...??

DonAntonio

Sorry we use 'j' instead of 'i' for imaginary numbers because i usually means current in electrical engineering. I am not doing electrical but i need to know the math apparently..

im not sure about z, i though z means the complex number.. i don't understand the q

The capital I is just supposed to represent the bar things on either side of the equation i forget what they are called..

 

[NascentOxygen]

Sorry we use 'j' instead of 'i' for imaginary numbers because i usually means current in electrical engineering. I am not doing electrical but i need to know the math apparently..

im not sure about z, i though z means the complex number.. i don't understand the q

The capital I is just supposed to represent the bar things on either side of the equation i forget what they are called..

Oh, well that's cleared that up!

So you are wanting to plot on the complex plane the set of points which satisfy

(i) magnitude(z+1+i)=2

(ii)magnitude(2z+3)≤1

I'm a bit rusty on z stuff myself. Let's start off by replacing z by x + iy

magnitude(x+iy+1+i) = 2

Collecting real and imaginary,
⇒magnitude({x+1} + i{1+y}) = 2

That's a single complex number inside the ( ). How do you write its magnitude?

 

[DonAntonio]

Sorry we use 'j' instead of 'i' for imaginary numbers because i usually means current in electrical engineering. I am not doing electrical but i need to know the math apparently..

im not sure about z, i though z means the complex number.. i don't understand the q

The capital I is just supposed to represent the bar things on either side of the equation i forget what they are called..

Wow, now I see...lol! Those bars, you should know, are called "absolute value" or "module of a complex number"...! So you actually meant to solve $$|z+1+i|=2$$$$|2z+3|\leq 1$$

Let $\displaystyle{z=a+bi\,,\,\,a,b\in\mathbb R}$ and substitute in the equations above.
Mod note: Removed a too-complete answer.
DonAntonio

 

[NascentOxygen]

DonAntonio, the philosophy of physics forums is to not provide a complete homework solution without encouraging some contribution from the OP. Despite its location in the general forum, this has every appearance of being a homework or assignment question.

And the word is "modulus".

 

[DeathNinja]

Wow, now I see...lol! Those bars, you should know, are called "absolute value" or "module of a complex number"...! So you actually meant to solve $$|z+1+i|=2$$$$|2z+3|\leq 1$$

Let $\displaystyle{z=a+bi\,,\,\,a,b\in\mathbb R}$ and substitute in the equations above.
Mod note: Removed a too-complete answer.
DonAntonio

DonAntonio, the philosophy of physics forums is to not provide a complete homework solution without encouraging some contribution from the OP. Despite its location in the general forum, this has every appearance of being a homework or assignment question.

And the word is "modulus".

Thank you so much DonAntonio. Though It would have been much better and less of a waste of your time if I could have seen the rest of your answer.

Moderator. Do you enjoy treating people like children?? This isn't high school homework! This is an example of a question which I didn't quite understand due to not being shown any examples at the night classes I attend to try and get my engineering degree. There will possibly be a similar question on the test,. Thanks for the hindrance in what is already a great challenge and the condescending attitude, I don't think there is any point being on this forum if its going to be so fascist.

 

[SammyS]

Thank you so much DonAntonio. Though It would have been much better and less of a waste of your time if I could have seen the rest of your answer.

Moderator. Do you enjoy treating people like children?? This isn't high school homework! This is an example of a question which I didn't quite understand due to not being shown any examples at the night classes I attend to try and get my engineering degree. There will possibly be a similar question on the test,. Thanks for the hindrance in what is already a great challenge and the condescending attitude, I don't think there is any point being on this forum if its going to be so fascist.

The moderator (who does his/her work here as a volunteer) was merely enforcing the rules of this Forum.

Physics Forum appears to be helpful to many of those who come here seeking help. We regret it if you feel you were not helped.

 

[NascentOxygen]

This is an example of a question which I didn't quite understand due to not being shown any examples at the night classes I attend to try and get my engineering degree.

Was my intro to help you get started with this example not sufficiently encouraging? https://www.physicsforums.com/showpost.php?p=3886532&postcount=4