Reputation
506
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
3 11
Newest
 Inquisitive
Impact
~7k people reached

  • 0 posts edited
  • 0 helpful flags
  • 97 votes cast
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 $7$?
Aug
1
comment Finding all the values of $\sqrt[3]{7-4i}$
What does $e^{i\theta}$ stand for? I've not come across this shorthand yet.
Aug
1
comment Finding all the values of $\sqrt[3]{7-4i}$
@Nameless Rewrite it using which formula? The only formula I have is finding the roots of 1.
Aug
1
asked Finding all the values of $\sqrt[3]{7-4i}$
Jul
30
awarded  Inquisitive