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x^2-4*i=0 equation

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Numerical solution:

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The solution

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 2          
x  - 4*I = 0
x2−4i=0x^{2} - 4 i = 0
Simplify
Detail solution
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=0b = 0
c=−4ic = - 4 i
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (-4*i) = 16*i

The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=2ix_{1} = 2 \sqrt{i}
x2=−2ix_{2} = - 2 \sqrt{i}
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−4iq = - 4 i
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=−4ix_{1} x_{2} = - 4 i
The graph
Rapid solution [src] 
         ___       ___
x1 = - \/ 2  - I*\/ 2
x1=−2−2ix_{1} = - \sqrt{2} - \sqrt{2} i 
       ___       ___
x2 = \/ 2  + I*\/ 2
x2=2+2ix_{2} = \sqrt{2} + \sqrt{2} i 
x2 = sqrt(2) + sqrt(2)*i
Sum and product of roots [src] 
sum
    ___       ___     ___       ___
- \/ 2  - I*\/ 2  + \/ 2  + I*\/ 2
(−2−2i)+(2+2i)\left(- \sqrt{2} - \sqrt{2} i\right) + \left(\sqrt{2} + \sqrt{2} i\right) 
=
0
00 
product
/    ___       ___\ /  ___       ___\
\- \/ 2  - I*\/ 2 /*\\/ 2  + I*\/ 2 /
(−2−2i)(2+2i)\left(- \sqrt{2} - \sqrt{2} i\right) \left(\sqrt{2} + \sqrt{2} i\right) 
=
-4*I
−4i- 4 i 
-4*i
Numerical answer [src] 
x1 = -1.4142135623731 - 1.4142135623731*i
x2 = 1.4142135623731 + 1.4142135623731*i
x2 = 1.4142135623731 + 1.4142135623731*i
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