Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 1

Solution

Factorize the following .

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Solution

Find roots using quadratic formula:z=−6±36−522=−6±−162=−6±4i2=−3±2iTherefore:z2+6z+13=(z−(−3+2i))(z−(−3−2i))=(z+3−2i)(z+3+2i)\begin{aligned} & \boxed{\text{Find roots using quadratic formula:}} \\ \\ & z = \frac{-6 \pm \sqrt{36 - 52}}{2} = \frac{-6 \pm \sqrt{-16}}{2} = \frac{-6 \pm 4i}{2} = -3 \pm 2i \\ \\ & \boxed{\text{Therefore:}} \\ \\ & z^2 + 6z + 13 = (z - (-3 + 2i))(z - (-3 - 2i)) \\ \\ & = (z + 3 - 2i)(z + 3 + 2i) \end{aligned}

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