Ext 2 Help. Simple one PLZ HELP!!!!!!!! (1 Viewer)

[mike7955]

z= 3+2i

1. Plot z in the complex plane
2. plot kz in the complex plane for k = 0, 1, 2, 3
3. Describe in words the set [kz : k∈ℤ]
4. Plot kz in the complex plane for all k∈ [-3, 3]
5. Describe in words the set {kz : k∈ℝ]
6. What would the set of numbers of the form kz look like, if k was allowed to vary over all possible complex numbers? Compare this with your answer to question 5.

I can do some but I don't understand some of the symbols and the wording of questions.

Can somebody please help me. Thanks!!!!!!!

 

[anomalousdecay]

Ok. The pitchfork looking E means that k is a z(complex number) or k is a real number.
First draw your imaginary axis in place of the y-axis. Keep the x-axis the same.
kz is a straight line with the same gradient (definition of a straight line). k represents multiples of z, where k=0 z=0, k=1 z=3+2i, k=2 z= 6+4i, k=3 z= 9+6i.
Do 4 the same way as 2, just extend the line.
For 3, 5 and 6, I would preferably let k=x+iy, then find kz as a locus. At the end of the answer, take the value in proportion.
For example, if k is a real number, then disregard any imaginary numbers for the locus.

I did my best.
This is an odd question. I use Cambridge and Terry Lee but I have never seen this type of question before.
By the way, what is your class up to in 4-unit. We have only finished Complex Numbers, Polynomials and Conics.

 

[seanieg89]

 

[anomalousdecay]

Ok that makes sense. Hopefully others will learn from my mistake.

By the way, for your Pure Mathematics course, what UAI did you need back then?
And when you finish what types of jobs are you looking to get.
I'm just asking because I was thinking of maybe doing a pure Mathematics and Engineering double degree.

Thanks.