Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.3

Question 1

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Factorize the following .

(v) z22z1z^2 - 2z - 1

Solution

Find roots using quadratic formula:z=2±4+42=2±82=2±222=1±2Therefore:z22z1=(z(1+2))(z(12))\begin{aligned} & \boxed{\text{Find roots using quadratic formula:}} \\ \\ & z = \frac{2 \pm \sqrt{4 + 4}}{2} = \frac{2 \pm \sqrt{8}}{2} = \frac{2 \pm 2\sqrt{2}}{2} = 1 \pm \sqrt{2} \\ \\ & \boxed{\text{Therefore:}} \\ \\ & z^2 - 2z - 1 = (z - (1 + \sqrt{2}))(z - (1 - \sqrt{2})) \end{aligned}