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 Feb 11 awarded Notable Question Nov 18 revised Finding cartesian equation from parametric trigonometric equations added 7 characters in body Nov 18 awarded Popular Question Sep 17 awarded Popular Question Aug 2 accepted Finding the functions for circular reflection and their inverted forms Aug 2 comment Finding the functions for circular reflection and their inverted forms @YvesDaoust I'm just trying to understand how you get $x'=\frac{x}{x^2+y^2}, y'=\frac{y}{x^2+y^2}$ in the first place. How you derive these formulae? Aug 2 comment Finding the functions for circular reflection and their inverted forms @HenningMakholm How does $\frac{1}{(x^2+y^2)^2}=\frac{x}{x^2+y^2}$? Aug 2 comment Finding the functions for circular reflection and their inverted forms No, my question was not about substituting in the numerator. I still don't understand how you arrive at $x'=\frac{x}{x^2+y^2}$ in the first place. Aug 2 comment Finding the functions for circular reflection and their inverted forms Won't $\lambda$ equal $\frac{1}{x^2+y^2}$ rather than $\frac{x}{x^2+y^2}$? Aug 2 comment Finding the functions for circular reflection and their inverted forms @HenningMakholm so would the inverse function of $x'$ be $x=\frac{x'}{x'^2+y'^2}$? Should it be $y^2$ or $y'^2$? Aug 2 asked Finding the functions for circular reflection and their inverted forms Aug 2 comment Verify that $\sqrt{1+\sqrt2+\sqrt3+\sqrt5}$ is constructible by determining the sequence of its extension fields I haven't used the $\subseteq \Bbb Q$ syntax before so I don't fully understand everyone's comments. Would you mind explicitly linking it to the idea of extending subfields with $k$ as above? Aug 2 asked Verify that $\sqrt{1+\sqrt2+\sqrt3+\sqrt5}$ is constructible by determining the sequence of its extension fields Aug 1 accepted Finding all the values of $\sqrt[3]{7-4i}$ Aug 1 comment Finding all the values of $\sqrt[3]{7-4i}$ Two final questions: 1) I'm not sure how to proceed to solve this, could you provide more help please? 2) In your first line, doesn't $\sqrt[3]{7-4i} = (7-4i)^{\frac{1}{3}}$? Aug 1 comment Finding all the values of $\sqrt[3]{7-4i}$ @Dr.SonnhardGraubner Does $k$ represent the amount of revolutions around the real axis? Aug 1 comment Finding all the values of $\sqrt[3]{7-4i}$ Okay, I understand. Is $\sqrt[3/2]{65}\left(\cos \frac{3\theta}{2} -i\sin\frac{ 3\theta}{2}\right)$ the final form, or do I have to link this with the values we attained for $\sin\theta$ and $\cos\theta$? Aug 1 comment Finding all the values of $\sqrt[3]{7-4i}$ I get that it's in the fourth quadrant, and only $\cos\theta$ can be positive. I don't understand why $65$ is the denominator rather than $\sqrt{65}$ Aug 1 comment Finding all the values of $\sqrt[3]{7-4i}$ Why does $\sqrt[3]{7-4i}=\left|\sqrt[3]{7-4i}\right|e^{\arg\left(\sqrt[3]{7-4i}\right)i}$‌​? I haven't used the $e^{arg}$ syntax before. Aug 1 comment Finding all the values of $\sqrt[3]{7-4i}$ Shouldn't $\sin\theta=\frac{4}{\sqrt{65}}$ and $\cos\theta=\frac{7}{\sqrt{65}}$, since the opposite side is $4i$ and the adjacent $7$?