Question

Simplify the expression
`(-5+i)/(2i)`. Explain

Answer 1

1/2 + 5/2 i

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