Question

Simplify the expression i}{2i}" alt="\frac{-5+i}{2i}" align="absmiddle" class="latex-formula">

Answer 1

Multiply by the conjugate and simplify.

1/2 + 5i/2

Answer 2

$\text{We know}\ i=\sqrt{-1}\to i^2=-1$

$\dfrac{-5+i}{2i}=\dfrac{-5+i}{2i}\cdot\dfrac{i}{i}=\dfrac{-5i+i^2}{2i^2}=\dfrac{-5i+(-1)}{2(-1)}=\dfrac{-5i-1}{-2}\\\\=\dfrac{-5i}{-2}+\dfrac{-1}{-2}=\boxed{\dfrac{1}{2}+\dfrac{5}{2}i}$