How can i factor $\displaystyle m^4 + 1 = 0 $???
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Originally Posted by tigergirl How can i factor $\displaystyle m^4 + 1 = 0 $??? Have you had any experience with complex numbers or de Moivre's theorem?
If you want to do it with real coefficients, you can't! But you can write $\displaystyle m^4+ 1= m^4- (-1)= (m^2)^2- (i)^2= (m^2- i)(m^2+ i)$ Now you can think of those as a difference of squares if you know the square roots of i and -i.
Originally Posted by tigergirl How can i factor $\displaystyle m^4 + 1 = 0 $??? The left hand side can be factored as two irreducible quadratic factors if you require real factors: $\displaystyle m^4 + 1 = m^4 + 2m^2 + 1 - 2m^2 = (m^2 + 1)^2 - 2m^2 = .... $
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