Solving for Z in a Complex Equation

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Homework Statement



Find z1,z2
z^2+iz+i=0

Homework Equations


How the quantity levels
Wanted to puts him in image most ease



The Attempt at a Solution



The beating in the enclosures other than glories
 

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I know that there are many people here who are weak in English but "The beating in the enclosures other than glories" completely mystifies me!

If you want to rewrite the solution if a+ bi form, I would recommend using DeMoivre's formula to find \sqrt{-1-4i} first.
 
m_s_a said:

Homework Statement



Find z1,z2
z^2+iz+i=0

Hi m_s_a! :smile:

z^2+iz+i=0 is an ordinary quadratic equation.

Solve it with the usual formula! :smile:
How the quantity levels
Wanted to puts him in image most ease

The beating in the enclosures other than glories


hmm … this makes no sense at all …

write it in your own language, and we'll tell you how to write it in English! :smile:
 
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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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