Any 2015s doing 4U maths? (Also 2015 4U maths thread) (2 Viewers)

[Carrotsticks]

I was asking out of sheer curiosity.
I have no idea how to visualize i^i.

Oh, I misunderstood the intend of your post.

I'll make a thread about it tonight if I have time.

 

[seanieg89]

I was asking out of sheer curiosity.
I have no idea how to visualize i^i.

Kind of related, but probably not a satisfactory answer to your question: http://community.boredofstudies.org...does-mean-have-irrational-complex-powers.html.

I don't know quite what you are hoping for in terms of a visualisation.

 

[braintic]

Kind of related, but probably not a satisfactory answer to your question: http://community.boredofstudies.org...does-mean-have-irrational-complex-powers.html.

I don't know quite what you are hoping for in terms of a visualisation.

Thanks for that. I'll have a read when I have time to absorb it, but all that is from a long time ago.
I'm not really sure myself what I mean by visualisation.
Perhaps I thought that as this seems to be a function which would be represented in 6 dimensions,

ie. x+iy = f(a+ib, c+id)
where f(m,n) = m^n

that maybe there are 2/3 D cross-sections that could be visualized to help build up a picture in my mind (other than the obvious boring ones).

 

[seanieg89]

Thanks for that. I'll have a read when I have time to absorb it, but all that is from a long time ago.
I'm not really sure myself what I mean by visualisation.
Perhaps I thought that as this seems to be a function which would be represented in 6 dimensions,

ie. x+iy = f(a+ib, c+id)
where f(m,n) = m^n

that maybe there are 2/3 D cross-sections that could be visualized to help build up a picture in my mind (other than the obvious boring ones).

Oh wow, okay yeah I see. Well its easy enough to understand the exp function graphically on the complex plane (its the familiar exponential on the real line and both real and complex part oscillate sinusoidally in the imaginary direction), so that is a start.

The logarithm is easy enough too, its real grows radially (in the same way the real logarithm grows), and its imaginary part grows as argument increases. (Keeping in mind that argument is multi-valued, so the imaginary part actually looks something like a staircase.)

These two things together give a pretty good idea of what exponentiation *looks* like.

 

[turntaker]

I want an e4 in ext 2. Can I for it

 

[b0b101]

got the 4 unit sweg started with graphs

 

[pzeait]

Any good youtube channels which teach the 4u course? Supposedly at the moment, harder 3 unit topics.

 

[turntaker]

Any good youtube channels which teach the 4u course? Supposedly at the moment, harder 3 unit topics.

Wootube