Question

Simplify the expression $\frac{-5+i}{2i}$. Explain

Answer 1

Answer:

1/2 + 5/2 i

Step-by-step explanation:

(-5+i)         i

---------* --------

2i             i

cannot have i in the denominator so we multiply by i

(-5+i)         i             -5i + i^2

---------* --------  = ----------------

2i             i              +2i^2

remember i^2 = -1

     -5i + -1        -1 -5i

= ---------------- = ------------------

    +2(-1)                        -2

get rid of the negative in the denominator by multiplying the top and bottom by -1

    (-1 -5i) * -1

= ------------------

          -2*(-1)

    (1 +5i)

= ------------------   =   1/2 + 5/2 i

          2