# Quadratic equations with imaginary numbers

Imaginary numbers and quadratic equations sigma-complex2-2009-1 Using the imaginary number iit is possible to solve all quadratic equations. ExampleUse the formula for solving a quadratic

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## Solving Quadratic Equations with Complex Number Solutions

Each side has a real part and an imaginary part. For the equality to hold, each of those must equal eachother. I.e. b 2 + 4 p = r 2 − s 2 ∧ 4 q i = 2 r s i From there, you can rewrite

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## Imaginary numbers and quadratic equations

P = (2 − i)(2 +i) = 4 +1 = 5. So the equation with these roots is: x2 −4x + 5 = 0. If we strictly answer the question and require imaginary roots then we have no real component so:

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Quadratic Equations with Complex (Imaginary) Roots

Because of this, Imaginary and complex numbers were created. By definition, i is that number, which when squared, yields -1. Since i^2 = -1, it must be true that (-i)^2 = -1 So we have i^2 = -1

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