Labelling Argand diagrams? (1 Viewer)

[rumbleroar]

Just a quick question (it seems a bit stupid) but how would you label an Argand diagram? For example, would I label the vector 1+i as (1,1) or (1,i) ?

I'm only asking because I've been told conflicting things.

Thanks in advance!

 

[QZP]

You would represent z=1+i as the point (1,1) on the Argand plane. This is because a complex number z is in the form x + iy with variable constants x, y and the axes of the Argand plane are Re(z)=x and Im(z)=y.
Hence, (1,1) would translate to: x = 1, y = 1 and thus z = 1+(1)i = 1+ i.
Otherwise, (1, 1i) translates to x = 1, y = 1i and thus z = 1+(1i)i = 0 which is clearly wrong. Alternatively, you can immediately see this is wrong since y is defined as a real number and y= 1i invalidates this.

Hope this clears everything.

Edit: Just realised you were asking for vectors. In that case I'd say 1+i only because I've never seen it the other way round.

 

[Makematics]

Just a quick question (it seems a bit stupid) but how would you label an Argand diagram? For example, would I label the vector 1+i as (1,1) or (1,i) ?

I'm only asking because I've been told conflicting things.

Thanks in advance!

Good q, and im not entirely sure myself. But i would think it would be (1,1), and thats not actually referring to the vector, but rather the actual point, or complex number. I mean that you write (1,1) at the actual point corresponding
to (1,1) on the argand diagram, rather than next to the vector going from the origin to the point.

Correct me if im wrong, my complex numbers are rusty.

 

[panda15]

I just write it as (1,1), but I also label the axis Imz and Rez, to cover both ways.

 

[braintic]

1+i for the vector; (1,1) for the point; and never (1,i).
In university maths vectors are often written as ordered pairs, but this is more like matrix notation which is not in our syllabus. I think if you labelled a vector that didn't start at the origin as (1,1) many teachers would consider it as incorrect because they are not familiar with uni maths. Complex numbers themselves are often written as ordered pairs without even referring to a diagram, but on the Argand diagram this is best reserved for the point representation only.

 

[rumbleroar]

Thanks guys! I usually label it (1,1) if I were to represent 1+i. (With axes as re(z) and im(z))

Just gotta get some clarification because my teacher writes (1,i) on the axes with y and x. Would that still be technically correct? Or is it better to stick with re(z) and im(z) and (1,1)?


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[rumbleroar]

Good q, and im not entirely sure myself. But i would think it would be (1,1), and thats not actually referring to the vector, but rather the actual point, or complex number. I mean that you write (1,1) at the actual point corresponding
to (1,1) on the argand diagram, rather than next to the vector going from the origin to the point.

Correct me if im wrong, my complex numbers are rusty.

Yes I meant the point sorry. I should've not mentioned the vector. Thanks for that


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[Makematics]

Thanks guys! I usually label it (1,1) if I were to represent 1+i. (With axes as re(z) and im(z))

Just gotta get some clarification because my teacher writes (1,i) on the axes with y and x. Would that still be technically correct? Or is it better to stick with re(z) and im(z) and (1,1)?


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No writing y is the same as writing Imz because Imz=Im(x+iy)=y

 

[braintic]

Thanks guys! I usually label it (1,1) if I were to represent 1+i. (With axes as re(z) and im(z))

Just gotta get some clarification because my teacher writes (1,i) on the axes with y and x. Would that still be technically correct? Or is it better to stick with re(z) and im(z) and (1,1)?


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Ahh but that's different. There is nothing wrong with marking the imaginary axis with -i, 0, i, 2i, 3i, etc. All you are saying then is that the points that you have marked represents those particular complex numbers. But I suspect more people use real numbers there.

Though I'm not sure why you would write (1,i) on the axes when it belongs somewhere in the 1st quadrant, so maybe I am misinterpreting.

 

[rumbleroar]

Ahh but that's different. There is nothing wrong with marking the imaginary axis with -i, 0, i, 2i, 3i, etc. All you are saying then is that the points that you have marked represents those particular complex numbers. But I suspect more people use real numbers there.

Though I'm not sure why you would write (1,i) on the axes when it belongs somewhere in the 1st quadrant, so maybe I am misinterpreting.

Sorry bad phrasing! It's like the point (1,i) with the axes x and y on the Argand diagram. (Strong ex1 student lolz) (if that makes any sense at all..)


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