Complex Numbers Anyone?

im sure this is basic stuff to some, but how do you put e^(2-7(pi)i) in the for a+bi?

also, how can i work out princible values of, for example, (1+i)^3/2??

thanks guys

Reply 1

username9816

Ollie

im sure this is basic stuff to some, but how do you put e^(2-7(pi)i) in the for a+bi?

also, how can i work out princible values of, for example, (1+i)^3/2??

thanks guys

is this University Level Maths Ollie?

Reply 2

Ollie

bono

is this University Level Maths Ollie?

uni level/ poss. further a maths

Reply 3

Alaric

Ollie

im sure this is basic stuff to some, but how do you put e^(2-7(pi)i) in the for a+bi?

also, how can i work out princible values of, for example, (1+i)^3/2??

thanks guys

First one,
use Euler's formula (e^(ix) = cos x + i sin x) after factoring out the real part of the exponent. That'll probably need some cancelling but should be easy enough as you have a pi in there.

Second, I'd cube the (1+i) as I'm sure you know how, then find the square root of what you have there, the following page should help you work that out: http://mathworld.wolfram.com/SquareRoot.html

hope that is some help

Alaric.

Reply 4

Unregistered

Just out of curiosity, why do engineers and computer scientists need to do stuff with the square root of negative one? I didn't think that could have any possible application to the real world.

Reply 5

fishpaste

So apparently this is coming onto the main Alevel syllabus next year when they move some of the topics around.

Reply 6

way2go

Harry Potter

Just out of curiosity, why do engineers and computer scientists need to do stuff with the square root of negative one? I didn't think that could have any possible application to the real world.

It's not that easy to explain why we sometimes encounter problems with complex roots, they just exist. Complex numbers might for example arise in maxwell equations, aerodynamics and vibrations (which I will be studying next term, lol).

Furthermore, complex numbers can also be used to solve very difficult integral equations by employing the Cauchy equation (I have read about this, but don't really know yet how it exactly works).

In fact, complex numbers are just an adoption to an earlier convention, which we like to call the decimal system. People often tend to think that the decimal system is definitive, but that's of course nonsense. It is a valuable asset in the attempt to describe the world around us, but it cannot describe every phenomenon (I believe that the theory of everything - some like to call this the superstring theory - cannot even be described by mathematics, but that we have to define a new, more advanced language to express the physical ideas). Therefore the decimal system needed - and perhaps will need again - some adjustments. One of them was the introduction of complex numbers.

Reply 7

Alaric

fishpaste

So apparently this is coming onto the main Alevel syllabus next year when they move some of the topics around.

Well on the whole P4 (Edexcel) complex numbers are so easy that they may as well, they teach it to natural scientists here in cam in one (maybe two was a while ago now) lectures.

Alaric.

Reply 8

fishpaste

Alaric

Well on the whole P4 (Edexcel) complex numbers are so easy that they may as well, they teach it to natural scientists here in cam in one (maybe two was a while ago now) lectures.

Alaric.

Yeah, I agree they're quite straight forward enough for alevel students. I found the style of question in P4 (OCR) a little challenging though, it often said things like "Explain how the loci of this and the loci of that show that the number Z has a real component -2" etc. A little more thinking required than the usual predictable Alevel question, I'd say.