Complex Exponential Function 1

[@mohfa1806]

Old but gold....i salute you sir

[@payaparapasu]

perfect video

[@BrodyPianist]

thanks heaps, just found your videos, the visualizations are extremely helpful for me

[@Khwartz]

Very Thanks, especially for using black board with green writing, So Good for the eyes :)

[@mattyhild1014]

If you're struggling with this video i highly recommend starting with 3blue1brown episode 3 & 4 of lockdown math. Explains the fundamentals.

[@x.m.caucase7841]

Even if I know those formulas very well, I still don't feel the relation between exponential function and cos and sin... it's really frustrating.

[@fitofight8540]

X.M. Caucase see Taylor series expansion for exponential and you will understand the connection

[@EduTech01]

iitg.vlab.co.in/?sub=59&brch=166&sim=618&cnt=1 dear caucase please visit this link and find couple of graphs at the end. Complex exponential signals are plotted. If you observe, the x axis of exponential signal represent cos and y axis of the curve show sin.

[@EduTech01]

kzbin.info/www/bejne/gZCmaJuqiL2CiLs This video will also help you grab the idea

[@mnada72]

In order to feel the relation , one way is to look at Taylor expansion of e^x and cos(x) and sin(x)

[@Bjowolf2]

Correction - that Greek letter is a Theta, not an Omega 😉

[@lighttangerinesky]

Your video was very clear to understand. Thank you

[@nelsonaleon]

Beter explanation ever, thanks

[@lena191]

real good! keep up the good work!

[@hassanmachlab5881]

WONDERFUL THANK YOU!

[@Sam_on_YouTube]

Is there a reason other than historical accident that i is such a big deal? It seems to be just a unit vector that is perpendicular to some unstated vector. Wouldn't it be theoretically better, albeit more difficult in some situations, to state your vectors at all times? Whether they be in the x or y direction or i? The square root of a negative unit vector is an orthagonal unit vector. Rotate the unit vector from the origin about an orthagonal vector twice and you get the negative of the unit vector, which is the geometroc definition of the square root of -1. But it need not be one particular vector called i, it can be done in any dimension. Using i makes things difficult if you are trying to develop formulas that go beyond 2 dimensions. If you use e^ip as an expression of tracing aroind a circle, and then try to go into another dimension and talk about spheres or conic sections, you have to be very careful. If instead of thinking of i as a number, we think of it as an arbitrary dimension, it is much easier to add more arbitrary dimensions as needed.

[@DfromBoston2]

Thank you, sensei!

[@truetruetruly2163]

e to the i omega? isn't it theta?

[@datakprosto123]

thank you!

[@ckhalifa_]

the complete formula is f(θ, k) = e^i(θ+2kπ)

[@mrboyban]

can you do a video about then? really struggling with expression (2-w)(2-w^2)(2-w^3) as omega w=e^ipi/5. Do you know anything that can help me evaluate as the answer should be 31.

[@oldcar8592]

This was a wonderful explanation. I do disagree with his statement starting at :28 that by looking at the magnitude of the coefficient of e^(i)(theta) on the left hand side of the equation that we know this describes a unit circle with magnitude 1 in the complex plane. I believe we can't know by observation alone that there is not a magnitude value other than 1 embedded in e^(i)(theta). After all, e^0 = 1, e^1 = 2.71828..., so who can say e^(i)(theta) doesn't have a coefficient other than 1 as part of it's value? Or even a varying magnitude value just as e with a varying real exponent varies?

[@TheGmr140]

complex exponentials used in communications: kzbin.info/www/bejne/sH_FiIefgKqfaZI&t

[@batuhanartan]

Well great video , thank you :) But still you haven't explain whats the relation between exponential and complex exponential ? You sad " have you ever thought about exponential, and it doesn't look like complex exponential graphs, it is just moving circle around", and you passed the explaination.

[@ckhalifa_]

Re(e^z) = e^x

[@ardaaksu5033]

Damn 8 years old