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1. Escribir los siguientes números imaginarios en imaginarios puros \( \begin{array}{l}\text { a. } \sqrt{-45} \\ \text { b. } \sqrt{-169} \\ \text { c. }-\sqrt{-72} \\ \text { d. } \sqrt{-625} \\ \text { e. }-\sqrt{-120} \\ \text { f. }-\sqrt{-49} \\ \text { 2. Escribe en forma de número complejo las siguientes expresiones. } \\ \begin{array}{ll}\text { a. } \sqrt{-17} & \text { b. } \sqrt{-100}-\frac{3}{7} \\ \text { c. } 10-\sqrt{-20} & \text { d. }-\sqrt{-60}-\frac{\sqrt{2}}{5} \\ \text { e. } 7+\sqrt{-144} & \text { f. } \sqrt{-400}+\frac{15}{8}\end{array}\end{array}> \)

Ask by Bradley Turner. in Colombia
Mar 08,2025

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1. **Escribir en forma de imaginarios puros:** **a.** \[ \sqrt{-45} = 3\sqrt{5}\,i \] **b.** \[ \sqrt{-169} = 13\,i \] **c.** \[ -\sqrt{-72} = -6\sqrt{2}\,i \] **d.** \[ \sqrt{-625} = 25\,i \] **e.** \[ -\sqrt{-120} = -2\sqrt{30}\,i \] **f.** \[ -\sqrt{-49} = -7\,i \] 2. **Escribir en forma de número complejo:** **a.** \[ \sqrt{-17} = 0 + \sqrt{17}\,i \] **b.** \[ \sqrt{-100} - \frac{3}{7} = -\frac{3}{7} + 10\,i \] **c.** \[ 10 - \sqrt{-20} = 10 - 2\sqrt{5}\,i \] **d.** \[ -\sqrt{-60} - \frac{\sqrt{2}}{5} = -2\sqrt{15}\,i - \frac{\sqrt{2}}{5} \] **e.** \[ 7 + \sqrt{-144} = 7 + 12\,i \] **f.** \[ \sqrt{-400} + \frac{15}{8} = \frac{15}{8} + 20\,i \]

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Para transformar los números imaginarios a imaginarios puros, recuerda que \(\sqrt{-a} = i\sqrt{a}\). Así que: a. \(\sqrt{-45} = 3i\sqrt{5}\) b. \(\sqrt{-169} = 13i\) c. \(-\sqrt{-72} = -6i\sqrt{2}\) d. \(\sqrt{-625} = 25i\) e. \(-\sqrt{-120} = -2i\sqrt{30}\) f. \(-\sqrt{-49} = -7i\) Ahora, para escribir los números en forma de número complejo: a. \(\sqrt{-17} = i\sqrt{17}\) b. \(\sqrt{-100}-\frac{3}{7} = 10i - \frac{3}{7}\) c. \(10-\sqrt{-20} = 10 - 2i\sqrt{5}\) d. \(-\sqrt{-60}-\frac{\sqrt{2}}{5} = -2i\sqrt{15} - \frac{\sqrt{2}}{5}\) e. \(7+\sqrt{-144} = 7 + 12i\) f. \(\sqrt{-400}+\frac{15}{8} = 20i + \frac{15}{8}\) Recuerda que los números imaginarios son una parte emocionante de las matemáticas, ¡como un gran misterio que resolvemos!

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