How do Complex Numbers relate to Real Signals? ("Best explanation EVER!")

Explains the link between sinusoidal signals (in the "real world") and complex numbers (in the "maths world"). One point to note is that I have used "j" for the complex variable, instead of "i" (which is more commonly used). This is because I am an electrical engineer, and we use "i" for electrical current, so we use "j" for the complex variable to avoid confusing ourselves (... except then of course it can be confusing for physicists and mathematicians! ... sorry about that, but it is just the way it is.) If you would like to support me to make these videos, you can join the Channel Membership, by hitting the "Join" button below the video, and making a contribution to support the cost of a coffee a month. It would be very much appreciated. Or by clicking here:    / @iain_explains   Check out my 'search for signals in everyday life', by following my social media feeds: Facebook: https://www.facebook.com/profile.php?... Instagram:   / iainexplains   Website: http://www.iaincollings.com Related videos: (see http://www.iaincollings.com) • Why are Complex Numbers written with Exponentials?    • Why are Complex Numbers written with Expon...   • Essential Maths Needed to Study Signals and Systems    • Essential Maths Needed to Study Signals an...   • What is Negative Frequency?:    • What is Negative Frequency?   • Visualising Complex Numbers with an Example    • Visualising Complex Numbers with an Example   • Fourier Transform Equation Explained    • Fourier Transform Equation Explained ("Bes...   • What Does "Linear Phase" Mean?    • What Does "Linear Phase" Mean?   • Is Phase important in the Fourier Transform?    • Is Phase important in the Fourier Transform?   • What are Voltage and Current in Electric Circuits? An Electrical Engineering Perspective.    • What are Voltage and Current in Electric C...   For a full list of Videos and Summary Sheets, goto: http://www.iaincollings.com .