What is (4+i)/(2-5i) ?

The solution to (4+i)/(2-5i) is 3/29+22/29 i

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simplify (4+i)/(2-5i)

simplify

\frac{4 + i}{2 - 5 i}

\frac{3}{29} + \frac{22}{29} i

Solution steps

\frac{4 + i}{2 - 5 i}

Multiply by the conjugate

\frac{2 + 5 i}{2 + 5 i}

= \frac{( 4 + i ) ( 2 + 5 i )}{( 2 - 5 i ) ( 2 + 5 i )}

Simplify

\frac{( 4 + i ) ( 2 + 5 i )}{( 2 - 5 i ) ( 2 + 5 i )} : \frac{3 + 22 i}{29}

= \frac{3 + 22 i}{29}

Rewrite in standard complex form:

\frac{3}{29} + \frac{22}{29} i

= \frac{3}{29} + \frac{22}{29} i

\frac{18 x ^{7} y ^{8}}{30 x ^{6} y ^{6}}

(- 32)^{\frac{3}{5}}

21 k^{2} + 20 k - 32 = - 7

\frac{1}{6} x - \frac{1}{2} (x - 1) = \frac{1}{2}

2 x^{2} = 6 x + 3