simplify 5/(2-7i)

Solution

simplify

\frac{5}{2 - 7 i}

\frac{10}{53} + \frac{35}{53} i

Solution steps

\frac{5}{2 - 7 i}

Multiply by the conjugate

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

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

Simplify

\frac{5 ( 2 + 7 i )}{( 2 - 7 i ) ( 2 + 7 i )} : \frac{10 + 35 i}{53}

= \frac{10 + 35 i}{53}

Rewrite in standard complex form:

\frac{10}{53} + \frac{35}{53} i

= \frac{10}{53} + \frac{35}{53} i

(- 3) (- 2) (- 5) (- 6)

z^{2} - 16

- 2 (x - 3)^{2}

x^{2} y^{2} (- 5 x^{2} y^{2})

(a^{2} + 2 ab - 2 b^{2}) (3 a - 7 b)