$\"\"$

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The equation is $\"\"$ .

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The solution is cube root of negative one.

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To find nth root of complex numbers, the complex number has trigonometric form.

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So the complex number change into trigonometric form.

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The complex number is $\"\"$ .

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The trigonometric form of complex number $\"\"$ is $\"\"$ . $\"\"$

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The absolute value (modulus) of $\"\"$ is $\"\"$ .

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The absolute value (modulus) of $\"\"$ is $\"\"$ .

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The reference angle $\"\"$ is given by $\"\"$ .

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The value of $\"\"$ and the complex number $\"\"$ lies in quadrant II ( $\"\"$ ).

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So, the angle is $\"\"$ .

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The trigonometric form of complex number $\"\"$ is $\"\"$ $\"\"$

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The solution is cube root of $\"\"$ .

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The nth root of complex number formula is $\"\"$ .

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$\"\"$ (Write solution in trigonometric form)

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$\"\"$ (Apply nth root formula)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify) $\"\"$

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So for $\"\"$ , the cube roots are as follows:

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$\"\"$ (Write trigonometric form of complex number)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify)

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$\"\"$ (Write trigonometric form of complex number)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify)

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$\"\"$ (Write trigonometric form of complex number)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify) $\"\"$

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The solutions are $\"\"$ .