What is (4-i)/(2+3i) ?

The solution to (4-i)/(2+3i) is 5/13-14/13 i

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simplify (4-i)/(2+3i)

simplify

\frac{4 - i}{2 + 3 i}

\frac{5}{13} - \frac{14}{13} i

Solution steps

\frac{4 - i}{2 + 3 i}

Multiply by the conjugate

\frac{2 - 3 i}{2 - 3 i}

= \frac{( 4 - i ) ( 2 - 3 i )}{( 2 + 3 i ) ( 2 - 3 i )}

Simplify

\frac{( 4 - i ) ( 2 - 3 i )}{( 2 + 3 i ) ( 2 - 3 i )} : \frac{5 - 14 i}{13}

= \frac{5 - 14 i}{13}

Rewrite in standard complex form:

\frac{5}{13} - \frac{14}{13} i

= \frac{5}{13} - \frac{14}{13} i

\frac{12 x}{5} = 18

- 3 x - 9 = - 45

a^{3} + 8 a^{2} - 84 a

16 x^{2} + 72 x + 81

\frac{1 - 3 i}{1 + i}