What is (4+7i)/(2+5i) ?

The solution to (4+7i)/(2+5i) is 43/29-6/29 i

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simplify (4+7i)/(2+5i)

simplify

\frac{4 + 7 i}{2 + 5 i}

\frac{43}{29} - \frac{6}{29} i

Solution steps

\frac{4 + 7 i}{2 + 5 i}

Multiply by the conjugate

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

= \frac{( 4 + 7 i ) ( 2 - 5 i )}{( 2 + 5 i ) ( 2 - 5 i )}

Simplify

\frac{( 4 + 7 i ) ( 2 - 5 i )}{( 2 + 5 i ) ( 2 - 5 i )} : \frac{43 - 6 i}{29}

= \frac{43 - 6 i}{29}

Rewrite in standard complex form:

\frac{43}{29} - \frac{6}{29} i

= \frac{43}{29} - \frac{6}{29} i

\frac{1}{tan ( x ) + cot ( x )}

- 6 x^{2} - 6 x + 12

(1 - x^{2})^{2}

(u^{2} - 1)^{3}

\frac{5 + i}{- 3 + 2 i}