Rewriting Complex Numbers Using the Complex Conjugate Method

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Shackleford
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How did they rewrite this?

A = 1 / (-2 + 4i)

A = -(1/10) - (1/5)i
 
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Multiply the numerator and denominator of A by the complex conjugate of -2 + 4i
 
Ed Aboud said:
Multiply the numerator and denominator of A by the complex conjugate of -2 + 4i

That's what I was thinking but wasn't sure. I haven't had to do that in a long time. lol.
 

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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