Geometric description homework

hsong9
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Homework Statement


In each case give a geometric description of the cosets of H in G.
a) G=R*, H=R+
b) G=C*, H=R

Homework Equations





The Attempt at a Solution


I have no idea about geometric description...
 
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R* means multiplicative
R+ means additive
left and right cosets...
 


The meanings of R* and R+ are clear - and since they are abelian it doesn't matter whether we mean left or right cosets.First, let's forget the geometric nature of the question. Instead, can you say what the cosets are in each case?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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