What is (3i)/(4-3i) ?

The solution to (3i)/(4-3i) is -9/25+12/25 i

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simplify (3i)/(4-3i)

simplify

\frac{3 i}{4 - 3 i}

- \frac{9}{25} + \frac{12}{25} i

Solution steps

\frac{3 i}{4 - 3 i}

Multiply by the conjugate

\frac{4 + 3 i}{4 + 3 i}

= \frac{3 i ( 4 + 3 i )}{( 4 - 3 i ) ( 4 + 3 i )}

Simplify

\frac{3 i ( 4 + 3 i )}{( 4 - 3 i ) ( 4 + 3 i )} : \frac{12 i - 9}{25}

= \frac{12 i - 9}{25}

Rewrite in standard complex form:

- \frac{9}{25} + \frac{12}{25} i

= - \frac{9}{25} + \frac{12}{25} i

80 \times 5

i 3 \cdot i 3

3024 \cdot \frac{3}{12}

- 97

1 0^{- 150 (20)^{46.801}}