Complex Analysis: Solving for P(z) When Z=a+bi

Daniel Monroy
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also P(z)=0, if it is, how is it related to Z=a+bi??
 
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It certainly depends on what P you have.
 
Daniel Monroy said:
also P(z)=0, if it is, how is it related to Z=a+bi??
Well, if P(z)= 0 and z= a+bi then P(a+bi)= 0. Other than that, I have no idea what you are talking about! What is "P"?
 

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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