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z^2+5=0

z^2+5=0 equation

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Numerical solution:

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The solution

You have entered [src] 
 2        
z  + 5 = 0
z2+5=0z^{2} + 5 = 0
Simplify
Detail solution
This equation is of the form
a*z^2 + b*z + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
z1=D−b2az_{1} = \frac{\sqrt{D} - b}{2 a}
z2=−D−b2az_{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=5c = 5
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (5) = -20

Because D<0, then the equation
has no real roots,
but complex roots is exists.
z1 = (-b + sqrt(D)) / (2*a)

z2 = (-b - sqrt(D)) / (2*a)

or
z1=5iz_{1} = \sqrt{5} i
z2=−5iz_{2} = - \sqrt{5} i
Vieta's Theorem
it is reduced quadratic equation
pz+q+z2=0p z + q + z^{2} = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=5q = 5
Vieta Formulas
z1+z2=−pz_{1} + z_{2} = - p
z1z2=qz_{1} z_{2} = q
z1+z2=0z_{1} + z_{2} = 0
z1z2=5z_{1} z_{2} = 5
The graph
012345-5-4-3-2-1020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
      ___       ___
- I*\/ 5  + I*\/ 5
−5i+5i- \sqrt{5} i + \sqrt{5} i 
=
0
00 
product
     ___     ___
-I*\/ 5 *I*\/ 5
−5i5i- \sqrt{5} i \sqrt{5} i 
=
5
55 
5
Rapid solution [src] 
          ___
z1 = -I*\/ 5
z1=−5iz_{1} = - \sqrt{5} i 
         ___
z2 = I*\/ 5
z2=5iz_{2} = \sqrt{5} i 
z2 = sqrt(5)*i
Numerical answer [src] 
z1 = -2.23606797749979*i
z2 = 2.23606797749979*i
z2 = 2.23606797749979*i
The graph
z^2+5=0 equation
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