Boone Clarke
05/02/2024 · High School
Find all the complex roots. Write the answer in exponential form. The complex cube roots of \( 3+3 i \). The complex cube roots are (Simplify your answers. Type exact answers, using \( \pi \) as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than \( 2 \pi \). Use integers or fractions f any numbers in the expression. Use a comma to separate answers as needed.)
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The complex cube roots of \( 3 + 3i \) are:
\[
\sqrt[3]{3} \cdot \sqrt[6]{2} e^{i\frac{\pi}{12}}, \sqrt[3]{3} \cdot \sqrt[6]{2} e^{i\frac{11\pi}{12}}, \sqrt[3]{3} \cdot \sqrt[6]{2} e^{i\frac{19\pi}{12}}
\]
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