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"Where" exactly are complex numbers used "in the real world"?
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 modulated by electromagnetic waves.
complex numbers - Parametrizing shapes, curves, lines in $\mathbb {C ...
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 point. As example, consider a square with in the Complex plane with vertices $ (0, 0), (1, 0), (1, 1), (0, 1)$.
What is the dot product of complex vectors?
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 product, if you don't generalize that definition as shown above.
complex numbers - What is $\sqrt {i}$? - Mathematics Stack Exchange
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 often as the square root of 2 does --- that is, it isn't rare, but it arises only because of our prejudice for things which can be expressed using small integers.
Do complex numbers really exist? - Mathematics Stack Exchange
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...
complex numbers - Why is $ |z|^2 = z z^* $? - Mathematics Stack Exchange
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?
Complex power of a complex number - Mathematics Stack Exchange
Complex power of a complex number [closed] Ask Question Asked 12 years, 1 month ago Modified 5 months ago
radicals - How do I get the square root of a complex number ...
The square root is not a well defined function on complex numbers. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number.
Equation of ellipse, hyperbola, parabola in complex form
Equation form 2:$$ (x-b)^2= 4 a y $$ Let z be a complex variable in a complex plane $\omega$, it is denoted by the following equation $$ z = x + i y $$ where x and y are real and imaginary parts of a complex variable which corresponds to Abscissa and Ordinate in analytical geometry and its conjugate $$\overline {z}= x - i y$$
complex numbers - Evaluating $\cos (i)$ - Mathematics Stack Exchange
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 between ordinary trigonometric functions, hyperbolic trigonometric functions, and complex logarithmic function.
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