How to find the square of a complex number?
Basic Question on the real and imaginary part of a complex number. 2.
Rotating a complex number - Mathematics Stack Exchange
2017年10月22日 · I have the complex number $3 + i$, and I am asked to get the complex number resulted by rotating the first one by $\frac{\pi}{4}$. I got the polar form of the first one to get its angle ($18.43°$) but when I add $\frac{\pi}{4}$ to it and …
How Do I Understand $e^i$, the Euler Form of Complex Number
2013年2月18日 · Each complex number is assigned a magnitude and an angle (called the argument). This is done precisely with the complex exponential. You may recall that multiplying two complex numbers is equivalent to rotating one number by the angle of the second (and then applying the proper stretches and compressions).
Calculating the reminder when dividing complex numbers
2014年8月7日 · When dividing complex numbers, let us consider $\\frac{26+120 i}{37+226 i}$. We multiply the numerator and denominator by $(37-226 i)$ and get the result, but how do I divide it like the normal divi...
Can a complex number be prime? - Mathematics Stack Exchange
2016年3月18日 · Yes, a complex number can be prime (in the traditional sense of the word). Recall that $\mathbb R \subseteq \mathbb C.$ Therefore, all numbers that you would traditionally think of as being prime are themselves complex (though not non-real).
What is the difference between complex numbers and 2D vectors?
2019年11月8日 · where the addition on the left hand side is complex number addition, and the addition on the left hand side is vector addition. And we could reverse the mapping and go from vector addition to complex number addition instead. We say that addition of complex numbers is isomorphic to addition of two dimensional vectors. Note that we are not saying ...
Positive and negative complex numbers? - Mathematics Stack …
2014年5月10日 · A complex number can be treated as a kind of multivector existing in a 2-d geometric algebra (GA). Seen this way, the answer to your question is that you can indeed negate complex numbers, much in the same way that multivectors (or …
Can a complex number ever be considered 'bigger' or 'smaller' …
2015年1月23日 · Observation: Many of the properties of the real number system $\mathbb{R}$ hold in the complex number system $\mathbb{C}$, but there are some rather interesting differences as well--one of them is the concept of order. The concept of order used in $\mathbb{R}$ does not carry over to $\mathbb{C}$.
How do I find the arctan of a complex number?
2023年11月30日 · I am trying to simplify $$\tan^{-1}\left(e^{ix}\right), x\in\mathbb{R}$$ $$=\\tan^{-1}\left(\cos x+i\sin x\right)$$ Using $$\tan^{-1}\left(a+b\right)=\frac12\tan^{-1 ...
Prove that $i^i$ is a real number - Mathematics Stack Exchange
$\begingroup$ @CameronBuie I agree for most practical purposes you don't need to distinguish but formally, since complex numbers and reals have different properties, do you have to do an intermediate conversion?