The non-real factors come in pairs which when multiplied give quadratic polynomials with real coefficients. Since every polynomial with complex coefficients can be factored into 1st-degree factors (that is one way of stating the ), it follows that every polynomial with real coefficients can be factored into factors of degree no higher than 2: just and quadratic factors. Complex conjugate, (or just the conjugate). Given the complex number = + the z a bi complex conjugate is denoted by and is defined to be, = + 8 = 0 3 cube of x3 x3 –8 → –8 → (x + 2)(x2 2x + 4) = 0 – + 2 = 0 or 2x + 4 = 0 x x2 – = or x –2 8 + 0 = 8 cis 180 i – Finding all the roots of a complex number nth From Polar-6 2 cis (30 + 0) 2 cis (30 + 90) 2 cis (30 + 180) 2 cis (30 + 270)
The non-real factors come in pairs which when multiplied give quadratic polynomials with real coefficients. Since every polynomial with complex coefficients can be factored into 1st-degree factors (that is one way of stating the ), it follows that every polynomial with real coefficients can be factored into factors of degree no higher than 2: just and quadratic factors. Complex conjugate, (or just the conjugate). Given the complex number z = a + bi the complex conjugate is denoted by and is defined to be, 3 cube of –8 → x3 = –8 → x3 + 8 = 0 (x + 2)(x2 – 2x + 4) = 0 x + 2 = 0 or x2 – 2x + 4 = 0 x = –2 or – 8 + 0 i = 8 cis 180 Finding all the nth roots of a complex number From Polar-6 2 cis (30 + 0) 2 cis (30 + 90) 2 cis (30 + 180) 2 cis (30 + 270)
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