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Quadratic Equations with Complex Coefficients

Consider the quadratic equation ax2 + bx + c = 0, where a, b, c are complex numbers and a ≠ 0.
Roots of equation are given by
α = 62558.png and β = 62552.png
These roots are complex as a, b, c are complex numbers.
Since the other relation is not defined in case of complex numbers, therefore we cannot assign positive or negative sign to the discriminant D = b2 – 4ac.
In case of quadratic equations with real coefficients imaginary (complex) roots always occur in conjugate pairs. However, it is not true for quadratic equations with complex coefficients. For example, the equation 4x2 – 4ix – 1 = 0 has both roots equal to 62545.png i.

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