Question

Why is exponential function for complex variable defined so?

Answer 1

what?

Answer 2

!!!!

Answer 3

Do you know the definition for exponential function for complex variable?

Answer 4

\[e^{i\theta} = \cos\theta + i\sin\theta\]?

Answer 5

\[e^{i\theta} = \cos\theta + i\sin\theta= z\]

Answer 6

Its not the exponential function for a complex variable. Its just another way to write a complex number.

Answer 7

no, I don't

Answer 8

then what is the exponential function for a complex variable?

Answer 9

Suppose \[z=x+iy\]
Then \[e^z=e^x(cos(y)+isin(y))\]

Answer 10

The text has turned to be too small, so I am writing it again
\[e^{x+iy}=e^x(cos(y)+isin(y))\]

Answer 11

are you getting me now?

Answer 12

By the way, did you all know the definition for the exponential function for a real variable?

Answer 13

Nope :-D

Answer 14

Suppose x is a real variable
Then
\[e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}....\]

Answer 15

This is it..

Answer 16

lol, that much we know

Answer 17

Now I hope you get my question?

Answer 18

I belive you are asking why is something true for real but now for complex?

Answer 19

If that is the definition for real variable, why is the definition for a complex variable such?

Answer 20

Not exactly that, I was asking the reason why the person who first defined that thing, defined it that way..

Answer 21

I mean why\[e^{x+iy}\] is equal to \[e^x(cos(y)+isin(y))\] and not something else?

Answer 22

I finally got you , hold on

Answer 23

http://www.youtube.com/watch?v=N4ceWhmXxcs

Answer 24

imranmeah91 - that is a good video! I loved it. Are you doing MIT Open Course Ware?

Answer 25

Hey Gt?

Answer 26

Hey Saifoo!

Answer 27

Hi, im really sorry i was unable to reply on fb, i just did now! ^_^

Answer 28

No worries. It was not an urgent issue.

Answer 29

BTW - I just got to "Super Hero" status. Fun! :-)

Don't know what it really means. But, interesting that I could get there in such a short time.

Answer 30

Congrats..
it's like for each 10 levels u will get new status..
But as more u go forward.. u need more points to get to another level.

Answer 31

Seems like it. Because at 50 level, it is slow moving to 51. However, I am surprised that it is not really based on difficulty of questions answered, but the number of questions answered.

Answer 32

Yes, Right.
that's how i got to 100. lol.

Answer 33

You guys are good and sharp on trignometry and calculus. I am really rusty (25 years ago done it). But, the point system works same for both.

Answer 34

Agree.. im leaning Calc 2 these days..

Answer 35

Let us keep in touch. I am going to sign off. Got to catch a plane tomorrow to California.

Answer 36

Oh, Kewl.
u may read the message!! ^_^

Answer 37

will do. bye.

Answer 38

Byee.

Answer 39

2b: thanks for the message. hopefully that video gives you what you need.