JemardBeejeez JemardBeejeez

09-07-2022
Mathematics

contestada

Evaluate the expression [tex]\sqrt[5]{3125{e}^{\frac{11 \pi }{2} i}}[/tex], leaving your answer in polar form.

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Medunno13 Medunno13

09-07-2022

[tex]\sqrt[5]{3125e^{\frac{11\pi}{2}i}}\\=\\\sqrt[5]{3125}\sqrt[5]{e^{\frac{11\pi}{2}}i}\\\\=5e^{\frac{11\pi}{10}i}\\\\\boxed{5\left(\cos \left(\frac{11\pi}{10} \right)+i \sin \left(\frac{11\pi}{10} \right) \right)}[/tex]

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