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 …

Jul 7, 2023 · First of all, complex numbers are two-dimensional, having independent x (real) and y (imaginary) components. This makes it possible to define a “rotation”, which you can't really do with …

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 …

Jun 9, 2011 · 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.

Jan 2, 2021 · With this in mind, I ask the following questions: Can the real numbers be said to be a subset of the complex numbers if complex numbers are defined as ordered pairs? If the complex …

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?

Jan 17, 2017 · Trigonometric functions for complex numbers Ask Question Asked 9 years, 1 month ago Modified 9 years, 1 month ago

Dec 23, 2014 · I am looking for an example explainable to someone only knowing high school mathematics why complex numbers are necessary. The best example would be possible to explain …

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 …

This is correct but: 1. in the complex numbers $\ln z$ is multivalued so which branch of $\ln z$ are we using here? and 2. the normal answer is $\tan x +C$ and how do we see that these two answers are …