What do you think is going to happen intuitively? 2 is a complex number with argument 0. What happens when you square it - what does its modulus become? What do you think will happen to the modulus of a general complex number in the specified region?

Reply 5

DFranklin

Original post by davros

Am I wrong to think that finding the argument of z^2 without understanding modulus argument form is a pretty big ask? I suspect the OP is supposed to know it...

Reply 6

B_9710

Have you covered De Moivre's theorem?

Reply 7

mqb2766

Original post by davidjohn03

No we haven’t done the exponential form

What have you covered? Could you upload a pic of the surrounding questions?

(edited 3 years ago)

Reply 8

old_engineer

Original post by davidjohn03

Can someone help with this Q please

This is a "state" question rather than a "show" or "derive" question, suggesting it's something you're supposed to know. With that in mind, your first port of call should be your textbook or class notes. But, having said that, it would do no harm for you to attempt to derive the modulus and argument of z^2, starting with z = a + bi.

(edited 3 years ago)

Reply 9

davidjohn03

No we haven’t covered de moivres theorum I’m guessing I’m probably not able to do this question then ? This is just the MEI AS practice papers .. the other qs are summation of series and sequences so unrelated but theres part2 to this Q if that helps 29D6339E-BD52-4966-A090-2A99DE3638C1.jpg.jpeg

29D6339E-BD52-4966-A090-2A99DE3638C1.jpg.jpeg

Reply 10

mqb2766

In asking for z^3 and z^4, the paper is expecting you to do it in polar/exponential form. If you've not covered it, maybe Google it? It's a very common representation for complex numbers. It even was a question on this week's university challenge.

Reply 11

davros

Original post by DFranklin

Am I wrong to think that finding the argument of z^2 without understanding modulus argument form is a pretty big ask? I suspect the OP is supposed to know it...

I was thinking along with the others that this should be assumed knowledge for a "state" question with few marks. But seeing some of the questions on here recently I do wonder what's being taught (or not, as the case may be).

Reply 12

DFranklin

Original post by davros

I think there are issues with syllabus changes and not a lot of papers/examples for the current syllabus, causing people to do questions from the old one or something.

But if you asked *me* to demonstrate arg z^2 without (even implicitly) writing z in arg/mod form I think I'd struggle.

Reply 13

davros

Original post by DFranklin

I can't even begin to separate things out because I was largely self-taught, so as long as I've known what a complex number was I think the mod-arg form was just something I absorbed before even understanding all the subtleties :smile:

Just playing about in my head I've realized that if z = x + iy then t = arg(z) means the same as tan t = y/x. Then tan(2t) = 2(y/x) / ( 1- (y/x)^2) = 2xy / (x^2 - y^2) which is just the arg of (x + iy)^2 = x^2 - y^2 + i(2xy), which is probably something I've also come across in my vast background reading. But as you say, not something you'd probably derive on the fly in an exam if you were new to complex algebra :biggrin:

Reply 14

DFranklin

Original post by davros

You've got the whole arctan(x/y) can differ from arg(x+iy) by pi to deal with as well. And the only "non-horrible" way I can see to deal with that is to say t = arg(x+iy) is the angle that makes x+iy = r(cos t + i sin t), at which point you've reinvented the mod/arg representation.