Question

Help simplifying the expression -5 + i/2i

Answer 1

is this (-5+i)/(2i)?

Answer 2

\[\frac{-5+i}{2i}?\]

Answer 3

Yes

Answer 4

ok and the objective i bet is to put into a+bi form

Answer 5

I think so

Answer 6

we know that i*i=i^2=-1
so to get rid of that imaginary unit in the denominator multiply both top and bottom by i

Answer 7

\[\frac{-5+i}{2i} \cdot \frac{i}{i} =?\]

Answer 8

what is (2i)*i=?
and what is (-5+i)*i=?

Answer 9

-5i -1 / -2 ?

Answer 10

\[\frac{-5i+i^2}{2i^2}=\frac{-5i-1}{-2}=\frac{-1-5i}{-2}\]
now there is a couple of more things to do to make it prettier

Answer 11

like all the terms on top and all the terms on bottom all have a -1 factor in common

Answer 12

\[\frac{(-1)(1+5i)}{(-1)(2)}=\frac{1+5i}{2}=\frac{1}{2}+\frac{5}{2}i\]

Answer 13

good job

Answer 14

i think im suppose to give and answer

Answer 15

what do you mean

Answer 16

the actual answer to -5 + i/2i not just putting it into a+bi form

Answer 17

a+bi is usually the standard form to put it into

Answer 18

The answer was -4.5 how do I get that

Answer 19

so when I asked you if it was \[\frac{-5+i}{2i}? \]
you didn't mean to answer yet right?

Answer 20

and you really meant \[-5+\frac{i}{2i}?\]
there is a difference between these fractions

Answer 21

oh okay nvm

Answer 22

\[-5+\frac{i}{2i} \\ -5+\frac{i}{2i} \cdot \frac{i}{i} \\ -5+\frac{i^2}{2i^2} \\ -5+\frac{-1}{2(-1)}\]
I think you can finish simplifying this

Answer 23

you could have just canceled the i's in the first step
-5+(1/2)