Polar Coordinates Homework: Understanding Second Equation

rsaad
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Homework Statement



In the attachment, I do not understand how we got the second equation in terms of polar coordinates.




Homework Equations





The Attempt at a Solution




I tried doing it by writing z_dot = (...)z and then plugging in r* exp i theta, but to no avail.
 

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rsaad said:

Homework Statement



In the attachment, I do not understand how we got the second equation in terms of polar coordinates.

Homework Equations


The Attempt at a Solution

I tried doing it by writing z_dot = (...)z and then plugging in r* exp i theta, but to no avail.

Show how you tried it. z'=r'e^(iθ)+iθ're^(iθ). Try going straight from the "complex notation" to the "polar notation". Divide both sides by e^(iθ) and equate real and imaginary parts.
 

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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