Answer
$1+2i$
Work Step by Step
Rationalize the denominator by multiplying the conjugate of the denominator, which is $2-i$, to both the numerator and the denominator:
$=\dfrac{5i(2-i)}{(2+i)(2-i)}
\\=\dfrac{10i-5i^2}{(2+i)(2-i)}$
Simplify using the rule $(a+b)(a-b) = a^2-b^2$ to obtain:
$=\dfrac{10i-5i^2}{2^2-i^2}
\\=\dfrac{10i-5i^2}{4-i^2}$
Use the rule $i^2=-1$ to obtain:
$=\dfrac{10i-5(-1)}{4-(-1)}
\\=\dfrac{10i-(-5)}{4+1}
\\=\dfrac{10i+5}{5}
\\=\dfrac{5+10i}{5}
\\=\dfrac{5}{5} + \dfrac{10}{5}i
\\=1+2i$
