Question

Simplify the expression.

-5+i / 2i

Any help would be amazing, thank you!

Answer 1

(-5 + i) / (2i ) i guess, maybe not, and are those just i's or root of -1

Answer 2

the way it is typed in is

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

Answer 3

@DanJS I'm sort of new to this site so I don't know how to type out equations in the proper format but, but it's -5 + i over 2i.

Like:

-5+i
_____
2i

I hope that makes sense!

And I think it's the root of -1. :)

Answer 4

If like that, I would excpet that i does denote \(\sqrt{-1}\).
What I would do is multiply times i on top and bottom to rationalize the denominator.

Answer 5

are the notifications not working on the site at the moment?

Answer 6

My reply notifications are a bit off, but message notificatios are on....

Answer 7

yeah, you don't want imaginary i on the bottom,
recall that i^2 = -1
and a complex number is in the form a + bi , a - bi

Answer 8

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

the i cancels in the second term, and need to multiply the first term by i / i
to get rid of that i in the bottom

Answer 9

I think I'm doing it wrong...can you check? @DanJS

So I tried following the steps you gave me and right now I'm at:

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

Am I doing it right? :(

Answer 10

Sorry that I'm kind of clueless. You could say math isn't exactly my strongest subject. :p

Answer 11

sorry, i am not receiving notifications at all

Answer 12

\[\frac{ -5 }{ 2i } * \frac{ i }{ i } + \frac{ 1 }{ 2 }\]

Answer 13

remember i^2 = -1 or i = root(-1)

That denominator in the first term is 2*i *i = 2*i^2 = 2* -1 = -2

Answer 14

\[\frac{ 5i }{ 2 } + \frac{ 1 }{ 2 }\]

Answer 15

that is it, if you want it in the normal form of a complex number a+bi, rearrange a bit

\[\frac{ 1 }{ 2 }+\frac{ 5 }{ 2 }i\]

Answer 16

I think I understand it now. You helped me a lot! Thank you so much, @DanJS!