Here are the essential concepts you must grasp in order to answer the question correctly.
Roots of Numbers
Roots are mathematical operations that determine a number which, when raised to a specific power, yields the original number. For example, the square root of 9 is 3, since 3² = 9. In this case, we are dealing with a sixth root, which means we are looking for a number that, when raised to the sixth power, equals -1.
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Real and Complex Numbers
Real numbers include all the numbers on the number line, encompassing both positive and negative values, as well as zero. However, certain roots, such as the sixth root of -1, do not yield real numbers. Instead, they fall into the category of complex numbers, which include imaginary units represented as 'i', where i² = -1.
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Introduction to Complex Numbers
Even Roots of Negative Numbers
When taking even roots (like square roots, fourth roots, etc.) of negative numbers, the result is not a real number. This is because no real number squared or raised to an even power can produce a negative result. Therefore, the sixth root of -1 is not a real number, but can be expressed in terms of complex numbers.
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Square Roots of Negative Numbers