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Imaginary numbers are involved in solving of the quadratic equations, when the discriminant of the equation is negative.
The quadratic equation:
ax^2 + bx + c = 0
x1 = [-b+sqrt(delta)]/2a
x2 = [-b-sqrt(delta)]/2a
Discriminant of the quadratic equation:
delta = b^2 - 4ac
If delta is negative, then sqrt -delta = i*sqrt delta.
We have used the property of imaginary unit i:
i^2 = -1
i = sqrt(-1)
We'll solve an example:
x^2 - 4x + 8 = 0
delta = (-4)^2 - 4*1*8
delta = 16 - 32
delta = -16
sqrt delta = sqrt (-1)*(16) = i*sqrt 16 = 4i
The roots of the quadratic equation are:
x1 = (4+4i)/2
x1 = 2 + 2i
x2 = 2 - 2i
We remark here the fact that if an equation has a complex root, then the equation has as root the conjugate of the complex root, also.
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