Answer
$\dfrac{3i}{5+i}=\dfrac{3}{26}+\dfrac{15}{26}i$
Work Step by Step
$\dfrac{3i}{5+i}$
Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator:
$\dfrac{3i}{5+i}=\dfrac{3i}{5+i}\cdot\dfrac{5-i}{5-i}=\dfrac{3i(5-i)}{5^{2}-i^{2}}=\dfrac{15i-3i^{2}}{25-i^{2}}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=\dfrac{15i-3(-1)}{25-(-1)}=\dfrac{15i+3}{25+1}=\dfrac{3+15i}{26}=\dfrac{3}{26}+\dfrac{15}{26}i$
