Im(Z)

[VCE_2012]

Is it 'improper' to label the Im(z) axis as: "...-2i,-i,0,i,2i,3i,4i...". I noticed the book uses just numbers without the 'i' accompanying it, but you can tell its an imaginary number anyway because of the axis it belongs to. But is it okay still to write"...-2i,-i,0,i,2i,3i,4i..." on the vertical axis? Yeah, its quite a lame question but I'm curious...

[pi]

It doesn't matter, but I use the 'i' just in case of a harsh examiner

But why would you label axis in such a way anyway? Usually in 'sketch' questions, labeling the axis with 1, 2, 0, -1, -2, etc. is unnecessary, you just label key points.

[luffy]

It doesn't matter, but I use the 'i' just in case of a harsh examiner

But why would you label axis in such a way anyway? Usually in 'sketch' questions, labeling the axis with 1, 2, 0, -1, -2, etc. is unnecessary, you just label key points.

To be honest, I disagree here. I think it is incorrect (not just improper) to use the 'i' if you were labelling the axes. The Im(z) axis details the imaginary part of the complex number a + bi. Im(z) in this particular complex number is equal to b, not "bi." Hence, the Im(z) values will never contain the 'i' term -->  including it is therefore, incorrect in my opinion. Though, I could be wrong.

Nonetheless, Rohitpi is probably right. Labelling the axis with -2,-1,0,1,2 seems redundant, unless the question said to "plot" the graph. In most cases, just use co-ordinates for key points instead.

[VCE_2012]

 That leads me to my next question:
When in an exam/exercises would you label the axis (1, 2, 0, -1, -2,) when it tells you to sketch many functions?
Because i just hate disproportional graphs... when two or more functions/points are required.

[luffy]

In an exam/exercise, I would not label the axis at all. The only points I label are the axis intercepts, turning points, asymptotes and obviously writing labelling which is Im(z) and which is Re(z). As I mentioned before, labelling the actual axis with no.s (i.e. -2,-1,0,1,2) is redundant and unnecessary.

This should work for 2 or more functions as well.

[ellecee]

I agree with luffy about not writing the 'i' as the Im(z) label on the axis already denotes it to be an imaginary number. On that note, never forget to label the axis!
Although it's unnecessary to label every number on the axis, I've heard from my Methods teacher that examiners are becoming fussier on scaling, so it's safer to at least mark one point on each axis to make the scaling clear. However, my teacher is quite a perfectionist and I'm not sure if it applies for GMA/Spesh.

[paulsterio]

To be honest, I disagree here. I think it is incorrect (not just improper) to use the 'i' if you were labelling the axes. The Im(z) axis details the imaginary part of the complex number a + bi. Im(z) in this particular complex number is equal to b, not "bi." Hence, the Im(z) values will never contain the 'i' term -->  including it is therefore, incorrect in my opinion. Though, I could be wrong.

Luffy is right here, it is mathematically incorrect to use the "i" term here, because a complex number, be definition, is x+yi, the function Re(x+yi) = x and Im(x+yi) = y
Hence, the axis should both be labelled as you would in a cartesian plane, except the axis will now be Re(z) and Im(z)

According to Wikipedia: "In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis.[1]"

It says that the imaginary PART (notice the word part) - is displacement (position with respect to the origin) - along the y-axis
This suggests that the y-axis should be marked with the displacements, which are the -3, -2, -1, 0, 1, 2, 3

Anyway, I personally label my axes if the graphs are:
a) Trigonometric/Circular Functions
b) Circles and Ellipses
c) Hyperbolas
...I can't even make a list

But its an instinctive feeling, it's like I label on a basis of where it would actually help me draw a graph, but then and again, i guess in an exam, it wouldnt hurt to label the axes, you cant lose marks for doing extra (provided it's right) - so why not!

[VCE_2012]

I agree with you.

[dc302]

If it says 'sketch' it simply means to sketch the shape of the graph and indicate any special points, such as points of intersection and maxima/minima etc. I would not label the axis, as if you do, you are suggesting your graph is drawn to scale, which it probably isn't.

[Special At Specialist]

In year 11/12 specialist maths, you are never expected to sketch entire functions purely on an argand diagram. They only ever ask you to plot points, so all you need to do is label the points.
Eg. if they said z = 1 + 2i and plot the point z^2, then you would plot the point (-3, 4). As luffy stated, you would NOT label it as (-3, 4i).