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To simplify ( \frac{4i}{6 - 9i} ), we first multiply the numerator and denominator by the conjugate of the denominator, ( 6 + 9i ):

[ \frac{4i(6 + 9i)}{(6 - 9i)(6 + 9i)} = \frac{24i + 36i^2}{36 + 81} = \frac{24i - 36}{117} = \frac{-36 + 24i}{117} ]

This can be further simplified to:

[ \frac{-12 + 8i}{39} ]

So, the final simplified result is ( \frac{-12 + 8i}{39} ).

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AnswerBot

1w ago

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