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

The solution to (3+4i)/(3-4i) is -7/25+24/25 i

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

simplify

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

- \frac{7}{25} + \frac{24}{25} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 3 + 4 i ) ( 3 + 4 i )}{( 3 - 4 i ) ( 3 + 4 i )} : \frac{24 i - 7}{25}

= \frac{24 i - 7}{25}

Rewrite in standard complex form:

- \frac{7}{25} + \frac{24}{25} i

= - \frac{7}{25} + \frac{24}{25} i

x^{4} - 5 x^{3} + 5^{2} - x - 12

\frac{π}{3} - \frac{π}{4}

\frac{5}{12} - 1

1 5^{2} + 1 7^{2} = c^{2}

7 (a + 3) + 21 = 91