You are Here: Home >< Maths

# Complex Numbers, Edexcel FP2. Sketching regions in an argand diagram, notation help. watch

1. Hi,

I have a query for exam purposes. I was wondering how the regions lying within and outside the circle boundaries are to be represented(shaded), when they have to include the boundaries and not include them i.e. strict inequalities and otherwise.

I encountered such an exercise in D1, where the strict inequalities were represented(shading was represented by putting tiny dashes on either side, according to requirement) with a dashed line. With regard to the FP2 exam, are the circles to be represented in the same way and what about the region/area inside the circles? Should it be shown using the same notation which was used for D1, which was simply putting tiny dashes on the side of the line which was to be excluded? It isn't shown this way in the book, but should I do it this way?

Does anyone have a sample that I could look at? Dashing circles and putting dashes for signifying the shaded region, is there a better way or is this the correct way?

The shading and sketching gets just a tiny little bit more complex because now they're circles, but I'm just wondering if they are to be dealt with in the same manner?
2. I was told by my teachers that it doesn't matter whether you shade inside or outside a region, so long as it's clear what region you're specifying (I normally just wrote a massive bold R inside the region).

More specifically, iirc, if the line or circle is not included in the region then I was told to use a normal line. If it was, then I'd use a dashed one. Again, it doesn't matter as long as it is clear from your working what you are doing and so long as your maths next to it remains consistent.
3. (Original post by wanderlust.xx)
I was told by my teachers that it doesn't matter whether you shade inside or outside a region, so long as it's clear what region you're specifying (I normally just wrote a massive bold R inside the region).

More specifically, iirc, if the line or circle is not included in the region then I was told to use a normal line. If it was, then I'd use a dashed one. Again, it doesn't matter as long as it is clear from your working what you are doing and so long as your maths next to it remains consistent.

O yeah, the bold R:!

Isn't it the oppositte way though? Isn't it dashed/broken lines for strict inequalities and normal lines for inequalities which are inclusive of the line?

EDIT: A better explanation for what I'm referring to can be seen in the answer at the back of the book for questions 1. (a.)(b.) [both parts of the first sum itself] for the exercise on sketching and representing regions, exercise 3G. It is a strict inequality but the circle and region is represented and drawn as including the boundary. By just looking at the answer and not the question, it is either incorrect or incomplete without writing , in words, that the region represents the area inside or outside the cirlce and NOT (explicitly) the boundary. Have a look. There isn't any maths/working that can be put down next to the diagrams, as you suggested.

The book has used dotted lines for the loci that is a perpendicular bisector and for straight lines/half lines (where strict inequalities are involved, example 32, part (a.ii), the only examply given in the book) however, sum 1 (d.) has an incorrect answer and I haven't checked the rest. It is a straight line loci and the inequality is strict. The region has been shown including the line/loci.

Circles however are exempt from being correctly demarcated in both the examples and the sums and corresponding answers.
4. (Original post by bomberdoom)

O yeah, the bold R:!

Isn't it the oppositte way though? Isn't it dashed/broken lines for strict inequalities and normal lines for inequalities which are inclusive of the line?

EDIT: A better explanation for what I'm referring to can be seen in the answer at the back of the book for questions 1. (a.)(b.) [both parts of the first sum itself] for the exercise on sketching and representing regions, exercise 3G. It is a strict inequality but the circle and region is represented and drawn as including the boundary. By just looking at the answer and not the question, it is either incorrect or incomplete without writing , in words, that the region represent the area inside or outside the cirlce and not the boundary. Have a look. There isn't any maths/working that can be put down next to the diagrams, as you suggested. Also in some questions, you have 3-4 equations and you have to specify one region in the diagram. The book has used dotted lines for the loci that is a perpendicular bisector and for straight lines. Circles however are exempt from being correctly demarcated.
Yeah, but you can clearly see which one is which. From the working out you can see which one's included and which one's excluded, etc. As long as the examiner knows what you're on about, you're fine. Just stay consistent (ie don't change from dashed to solid or from shading outside to inside willy nilly).
5. I can't make out, the boundary isn't demarcated as being exempt from the shaded region.

Part (c.) in the first sum itself has been represented the same way as the circles in part (a.) and (b.) and the inequation (the question) does not contain a strict inequality, the first two questions do.
|z+7| >_ |z-1| {>_ is more than equal to ... }

So there is no dotted/dashed line in that question's answer. The first two questions contain a strict inequality, and a continuous, normal, undashed/unbroken, line as in part (c.) has been drawn.

The circles seem ot be exempt from this rule. Notationally, the answers do not make sense, as in they are incorrect or they do not represent the equation in the question.

Anyhow, the problem does not lie with these questions, as a simple statement under the diagram, specifying whether the boundary is included or not, solves the issue, like it has been wrtten in those helpful rectangular yellow boxes on the side of the examples.
The problem lies when there are 3-4 equations and you have to label the Region R common to all equations. So instead of representing it properly, as in having the proper notation, you're resorting to long statements to make up for the inaccuracies of the diagram.

I hope you've been able to uderstand the above, however, I'm just interested in how it is to be done for the exams. Suppose I get a question with two circles. represent by complex numbers, and one has a strict inequality and one does not, then? It is weird to represent them in the same way.
For e.g. question 1.e. except that |z|<3 and not |z|<_3..so the question becomes.. 2 <_ |z| < 3 .

I've attached the answer below. If i write the same answer, for a question which is similar and has a strict inequality then the diagram stops being correct doesn't it?

I've posted answers to part (a.) and (b.) as well, look at the example for that exercise, only one has been give, example 32. Part (a.)(ii) it is a stric inequality and it has been shown with a dotted/dashed line.
Attached Images

6. Hey, no reply, I really need this sorted as I need to practice. I'm sort of stuck on Complex Numbers until I understand this hiccup. I think I haven't been clear in my above post, but it's difficult to explain tiny bits sitting behind a screen. However, again, how would I sketch the two following equations?

|z|<3 and |z| <_ 3 (less than equal to 3 in the second one)

They're both the same loci, but not the same inequality.

I don't have a problem with whether to sketch inside or outside as wanderlust.xx pointed out above, or which region to mark or sketch. My concern is, won't both the answers for |z|<3 and |z| <_3 look the same by the instructions given in the book? As in, there is a strict difference in the inequality, and how would that difference be shown/demarcated on the diagram?

Please try and post if you have can help in any way.

EDIT: AHH! I've been trying to crack every sum myself, but I finally looked into the solution bank and found it. The answers at the back of the book don't show the circles and regions like this. I've attached the file below. It's a perfectly dashed circle. I just need to reduce the wonkiness of my circles now.
However, I think wanderlust.xx is right, with proper working and one odd written statement stating that it is the interior/exterior region excluding or including the boundary is good enough as well along with the bold R. I also use a tiny, staight sharp arrow pointing from the equation to inside of the circle on the diagram. Like in the attachment below, where the equation is written, i draw a tiny arrow to the inside of the circle from the equation. Though it is unecessary with the bold R and shading with a ruler, it helps with sketches in general. I saw this done alot (the arrow bit) in C1/2/3 when the diagrams/sketches became cramped and coordinates of points needed to be specified which were close to each other or otherwise or when it was hard to fit them all in.

Thanks again wanderlust.xx for replying, good luck with your work and exam.
Attached Images

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 29, 2011
Today on TSR

### Are you living on a tight budget at uni?

From budgets to cutbacks...

### University open days

1. University of Edinburgh
Sat, 22 Sep '18
2. University of Exeter
Sat, 22 Sep '18
3. Loughborough University
Sat, 22 Sep '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams