Rationalize the denominator of square root of negative 9 over open parentheses 4 minus 7 i close parentheses minus open parentheses 6 minus 6 i close parentheses.

The answer is
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Before we rationalize the denominator, we must simplify the numerator and denominator.  We evaluate the square root on the top, and combine like terms on the bottom:


To rationalize the denominator, we multiply by the conjugate.  The conjugate is found by making the imaginary term of the complex number, the i part, the opposite sign.  The conjugate of -2-i is -2+i: