In order to simplify the expression, let's divide each term in the numerator by the denominator:
[tex]\frac{-5+i}{2i}=\frac{-5}{2i}+\frac{i}{2i}=-\frac{5}{2i}+\frac{1}{2}[/tex]Then, to remove the complex number i from the denominator of the first fraction, let's multiply the numerator and denominator by i:
[tex]-\frac{5}{2i}+\frac{1}{2}=-\frac{5\cdot i}{2i\cdot i}+\frac{1}{2}=\frac{-5i}{2i^2}+\frac{1}{2}=\frac{-5i}{2\cdot(-1)}+\frac{1}{2}=\frac{-5i}{-2}+\frac{1}{2}=\frac{5}{2}i+\frac{1}{2}[/tex]Therefore the complex number in the form a + bi is equal to 1/2 + (5/2)i.
