What is a Complex Exponential?

[@BitterTast3]

This is the first time I've seen the cosine and sine components visualized, thanks!

[@MarkNewmanEducation]

You're welcome.

[@piyush1365]

No one has ever explained the complex numbers and fourier transforms as you have. Great to have subscribed to you!

[@MarkNewmanEducation]

Welcome aboard! Really glad you found it useful. Check out my website for more: howthefouriertransformworks.com/

[@pavansai4572]

love u sir ..I don't know what to say, but very first time i know now that why to look into complex because its existed along with what we see, so when we go into deep with dimensions that everything is complex in nature ,i am writing this because i always have a bunch of questions on why this complex maths comes into my life and i don't know how think about it but it is everywhere ..now i felt really great about fourier that the idea of processing signals ,analysing a signal by multiplying with real and imaginary part to look into real analysis(time) and complex analysis (frequency) .at the moment i dont know what other things exist in complex but why he choose e^ix to study ..my dream is to become DSP engineer ..

[@laurenceo2340]

Thank you 🙏 another great video

[@wag-on]

Nice visualization.

[@jasonbourn29]

Great videos sir post mire videos and shorts

[@elijahjflowers]

🌀

[@shortplus001]

Sir what is fowrier series🎉 Please Explain a new video please

[@vinodbhatt7581]

Sir why Laplace transform is from 0 to infinity

[@MarkNewmanEducation]

Laplace Transforms are often used to study how a system responds to an I put. That input is typically said to occur at time=0. Before the input occurs, the response is of no interest. Laplace can be used to perform a number of different types of analysis. Here are a few examples. Steady-State Analysis: In many engineering and scientific problems, we are interested in understanding how a system behaves after it has settled into a stable state. This is often referred to as the "steady state." By taking the Laplace transform from 0 to infinity, you effectively focus on the long-term behavior of the system, which can simplify the analysis. Transient Response Elimination: The Laplace transform from 0 to infinity ignores the initial conditions and transient behavior of the system. Transients are temporary responses that occur when a system is subjected to a sudden change, and they eventually die out over time. By focusing on the Laplace transform in this range, you can isolate the system's response after these transients have disappeared. Frequency Domain Analysis: The Laplace transform allows you to analyze a system's behavior in the frequency domain. When you compute the Laplace transform from 0 to infinity, you obtain the frequency response of the system, which is valuable for understanding how the system reacts to different input frequencies.

[@Krageon-Offline]

Why do we use e for it? What’s so special about e that it connects real and imaginary numbers?

[@charlie-zm5wv]

讲得太好了！我这种文盲都能听懂，原来弹簧就是e*ix，回去我拆一个看看

[@MarkNewmanEducation]

Thank you. A spring is indeed a good analogy for e**ix. I hope you succeed with your experiment.