Mister Exam

Other calculators

k^2+1=0 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src]
 2        
k  + 1 = 0
$$k^{2} + 1 = 0$$
Detail solution
This equation is of the form
a*k^2 + b*k + c = 0

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

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

Because D<0, then the equation
has no real roots,
but complex roots is exists.
k1 = (-b + sqrt(D)) / (2*a)

k2 = (-b - sqrt(D)) / (2*a)

or
$$k_{1} = i$$
Simplify
$$k_{2} = - i$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 0$$
$$k_{1} k_{2} = 1$$
Rapid solution [src]
k1 = -I
$$k_{1} = - i$$
k2 = I
$$k_{2} = i$$
Sum and product of roots [src]
sum
0 - I + I
$$\left(0 - i\right) + i$$
=
0
$$0$$
product
1*-I*I
$$i 1 \left(- i\right)$$
=
1
$$1$$
1
Numerical answer [src]
k1 = -1.0*i
k2 = 1.0*i
k2 = 1.0*i