Question - Understanding Complex Numbers and Inequalities
Solution:
The expression in the image includes the square root of a negative number: $$-\sqrt{86}$$. In the realm of real numbers, you cannot take the square root of a negative number, as square roots are defined only for non-negative numbers. However, in the context of complex numbers, the square root of a negative number is a multiple of the imaginary unit $$i$$, where $$i$$ is defined as $$i^2 = -1$$.Thus, $$-\sqrt{86}$$ in terms of complex numbers is $$-i\sqrt{86}$$. This number is purely imaginary, and there is no real number less than or greater than it because comparisons of greater or less than do not apply to imaginary numbers.Therefore, the blank boxes on both sides of $$-\sqrt{86}$$ cannot be filled with real numbers to create a true statement about inequalities. Filling these blanks would require a context where complex numbers are included, and even then, the notion of "greater than" or "less than" isn't meaningful in the same way as it is with real numbers.
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