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

The solution to (2+5i)/(2-5i) is -21/29+20/29 i

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

simplify

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

- \frac{21}{29} + \frac{20}{29} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 2 + 5 i ) ( 2 + 5 i )}{( 2 - 5 i ) ( 2 + 5 i )} : \frac{20 i - 21}{29}

= \frac{20 i - 21}{29}

Rewrite in standard complex form:

- \frac{21}{29} + \frac{20}{29} i

= - \frac{21}{29} + \frac{20}{29} i

2 x^{2} - 11 x y + 5 y^{2}

3 (\frac{3}{2})

8 \cdot 12

z^{8} - 12 z^{4} + 35

(\frac{2 x ^{- 2} y ^{3}}{3 x y ^{- 4}})^{4}