Answer
$\dfrac{6+5i}{6-5i}=\dfrac{11}{61}+\dfrac{60}{61}i$
Work Step by Step
$\dfrac{6+5i}{6-5i}$
Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator:
$\dfrac{6+5i}{6-5i}=\dfrac{6+5i}{6-5i}\cdot\dfrac{6+5i}{6+5i}=\dfrac{(6+5i)^{2}}{6^{2}-(5i)^{2}}=...$
$...=\dfrac{6^{2}+2(6)(5i)+(5i)^{2}}{36-25i^{2}}=\dfrac{36+60i+25i^{2}}{36-25i^{2}}=...$
Substitute $i^{2}$ with $-1$ and simplify:
$...=\dfrac{36+60i+25(-1)}{36-25(-1)}=\dfrac{36+60i-25}{36+25}=\dfrac{11+60i}{61}=...$
$...=\dfrac{11}{61}+\dfrac{60}{61}i$
