How do you divide (6+5i)/(6-5i)?

Jul 14, 2015

Multiply numerator and denominator by the complex conjugate of the denominator to find:

$\frac{6 + 5 i}{6 - 5 i} = \frac{11 + 60 i}{61}$

Explanation:

$\frac{6 + 5 i}{6 - 5 i}$

$= \frac{\left(6 + 5 i\right) \left(6 + 5 i\right)}{\left(6 - 5 i\right) \left(6 + 5 i\right)}$

$= \frac{36 + 60 i - 25}{36 + 25}$

$= \frac{11 + 60 i}{61}$