Real and Imaginary Parts of z+(1/z) - Have I Got This Right?

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Hi there have i got this right if someone could check please? z=x+\imath{}y Find the real and imaginary parts z+(1/z) sub x+\imath{}y + \frac{1}{x+\imath{}y} if we multiply by x+\imath{}y and i get as the real part as x^2-y^2+1. Have i got this right? Thanks in advance
 
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No. First step.. I'd deal with the fractional part. Multiply the numerator and denominator by the complex conjugate of the denominator, and simplify. That's how you divide by a complex number anyway..
 
cheers mate
 

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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