Jan 24, 2013 · 50 Complex numbers are used in electrical engineering all the time, because Fourier transforms are used in understanding oscillations that occur both in alternating current and in signals …

Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obviou...

Feb 24, 2015 · Your second question was how does one go about parametrizing in the Complex plane. Draw the plot. Determine the direction of motion--counter clockwise or clockwise. Pick a starting …

May 12, 2015 · The square root of i is (1 + i)/sqrt (2). [Try it out my multiplying it by itself.] It has no special notation beyond other complex numbers; in my discipline, at least, it comes up about half as …

Oct 6, 2017 · This complex "dot product" is sometimes called a Hermitian form. This specific separate term serves as a way to make it clear that it might not comply with the usual definition of a dot …

Nov 27, 2020 · Then it is well defined on the complex plane as well and Euler's formula gives us its real and imaginary parts. However Euler's formula still valid for any complex number and makes bridges …

They're respectively addition and multiplication. For these two mappings the axioms of a field are satisfied (why?). The field thus written is what is called the field of the complex numbers $\mathbb …

Mar 5, 2020 · We can do calculus with complex numbers (differentiation and integration), unlike $\Bbb {R}^2$ (actually, we can differentiate in $\Bbb {R}^2$, but it is a different notion to differentiation with …

May 9, 2014 · I've been working with this identity but I never gave it much thought. Why is $ |z|^2 = z z^* $ ? Is this a definition or is there a formal proof?

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