Answer
$\dfrac{4-5i}{2i}=-\dfrac{5}{2}-2i$
Work Step by Step
$\dfrac{4-5i}{2i}$
Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator:
$\dfrac{4-5i}{2i}=\dfrac{4-5i}{2i}\cdot\dfrac{-2i}{-2i}=\dfrac{-2i(4-5i)}{-4i^{2}}=\dfrac{-8i+10i^{2}}{-4i^{2}}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=\dfrac{-8i+10(-1)}{-4(-1)}=\dfrac{-10-8i}{4}=-\dfrac{10}{4}-\dfrac{8}{4}i=-\dfrac{5}{2}-2i$
