The Mysteries of Complex Numbers

[Mu naught]

When do you become introduced to complex numbers? For example, raising functions to the power i or inputting i into trig functions etc...

I know they are used widely in physics, but when are you supposed to learn about them? None of the courses at my school up to and including diff Eq mention any complex stuff...

 

[ZippyDee]

You will usually go into complex numbers around Algebra II (or whatever the course is called for you). I don't know how likely it is that you would go as far as complex trig or complex exponents, but you might.

 

[HallsofIvy]

Most people are introduced to "complex numbers", though not generally to difficult computations such as transcendental functions of complex numbers, in about the 9th or 10th grades. A complete course in functions of complex numbers would probably be an upper division college course. I would be very surprised if a course in differential equations did not at least note that e^{ix}= cos(x)+ i sin(x). How else would you deal with y"+ y= 0?

 

[sachinism]

Most people are introduced to "complex numbers", though not generally to difficult computations such as transcendental functions of complex numbers, in about the 9th or 10th grades. A complete course in functions of complex numbers would probably be an upper division college course. I would be very surprised if a course in differential equations did not at least note that e^{ix}= cos(x)+ i sin(x). How else would you deal with y"+ y= 0?

well here , its only after 10th grade that the studentsa re generally introduced to the concept of complex numbers

and i really find it interesting the way people come out with interesting theoretical questions regarding the chapter

 

[Mu naught]

please don't patronize me... I am a 2nd year college student and I have never been taught any math involving complex numbers, aside from the fact that i = sqrt(-1).

I will be taking differential equations next semester and have yet to see any mathematics involving complex numbers. I want to know what college courses deal with these.

 

[rogerswd]

Its depend on your college course pattern or your teacher. I have studied complex numbers in 8th class.
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[awkward]

Mu naught,

Some differential equations books start out with complex numbers from the start, which I think is really the best way because it simplifies things a lot. But others don't use the complex numbers at all, which is the way DE was taught in the class I took long, long ago.

I haven't been in a classroom for a long time, but my guess is that if you haven't seen the complex numbers yet, you probably won't see much of them until you take a course in complex variables, although you ought to be at least introduced to their algebraic aspects when you take a class in algebra (of the groups, rings, fields variety). Which is a little sad, because a touch of complex variables can really simplify things occasionally. And it's a really beautiful subject, too. If you would like to take a sneak peak, pick up a complex variables text sometime and look at the first chapter or so. A lovely, but slightly unconventional, text is "Visual Complex Analysis" by Needham. He works out all the details of the complex functions like e^z etc. in great detail.

 

[Mu naught]

Mu naught,

Some differential equations books start out with complex numbers from the start, which I think is really the best way because it simplifies things a lot. But others don't use the complex numbers at all, which is the way DE was taught in the class I took long, long ago.

I haven't been in a classroom for a long time, but my guess is that if you haven't seen the complex numbers yet, you probably won't see much of them until you take a course in complex variables, although you ought to be at least introduced to their algebraic aspects when you take a class in algebra (of the groups, rings, fields variety). Which is a little sad, because a touch of complex variables can really simplify things occasionally. And it's a really beautiful subject, too. If you would like to take a sneak peak, pick up a complex variables text sometime and look at the first chapter or so. A lovely, but slightly unconventional, text is "Visual Complex Analysis" by Needham. He works out all the details of the complex functions like e^z etc. in great detail.

thanks for the advice

 

[HallsofIvy]

please don't patronize me... I am a 2nd year college student and I have never been taught any math involving complex numbers, aside from the fact that i = sqrt(-1).

I will be taking differential equations next semester and have yet to see any mathematics involving complex numbers. I want to know what college courses deal with these.

I certainly didn't mean to patronize you! I, myself, met complex numbers in a grade 11 class in high school. I have taught "complex numbers" in a first year college "PreCalculus class" as well as giving a quick review in "Calculus". I suspect that you will be expected to know at least the basics of complex numbers, though not necessarily anything to do with "analytic functions", in your differential equations course. If you do not know that, I recommend you talk to your differential equations instructor. Perhaps he/she can recommend readings for you.