Respuesta :

[tex]i^{13}[/tex]

[tex]\begin{gathered} i=\sqrt[]{-1} \\ So \\ i^2=-1 \end{gathered}[/tex][tex]\begin{gathered} \text{Express:} \\ i^{13} \\ As \\ i^{13}=i^2\cdot i^2\cdot i^2\cdot i^2\cdot i^2\cdot i^2\cdot i \end{gathered}[/tex][tex]\begin{gathered} i^{13}=(-1)\cdot(-1)\cdot(-1)\cdot(-1)\cdot(-1)\cdot(-1)\cdot i \\ i^{13}=1\cdot i \\ i^{13}=i \end{gathered}[/tex]

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[tex]\begin{gathered} \sqrt[]{-49} \\ \text{Use this property:} \\ \sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b} \\ So\colon \\ \sqrt[]{-49}=\sqrt[]{49\cdot(-1)}=\sqrt[]{49}\cdot\sqrt[]{-1} \\ \text{Where:} \\ \sqrt[]{49}=7 \\ \sqrt[]{-1}=i \\ so\colon \\ \sqrt[]{49}\cdot\sqrt[]{-1}=7i \end{gathered}[/tex]

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