Question

simplify the expression below

Answer 1

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

Answer 2

Multiply the top and bottom by i

Answer 3

\[\frac{ -10i+2i }{ 4i }\] i tried, but i have no idea if thats right though..

Answer 4

oh wait i wasnt supposed to multiply by 2i???

Answer 5

You can but the 2 will can be factored out and canceled. So multiply by i is better.
Also i times i = i squared = -1

Answer 6

@agent0smith

Answer 7

im still confused!

Answer 8

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

Answer 9

\[i = \sqrt{-1}\]\[i ^{2} = -1\]

Answer 10

i^2 = -1.
then as ranga put just simplify the values from there
-5i + (-1) / 2(-1)

Answer 11

ok i understand that part, im just exactly sure how to simplify it now.

Answer 12

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

Answer 13

how did they become positive?

Answer 14

Factor out -1 from top and bottom and they will cancel out.

Answer 15

For example: -5 / -3 = 5 / 3

Answer 16

how did you get the three?

Answer 17

I was just giving an example of dividing two negative numbers and how the negatives will cancel out.

Answer 18

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

Answer 19

now what do i do?

Answer 20

That is it. You have simplified the expression. You have gotten rid of the i in the denominator.

Answer 21

there is nothing more that you can do to simplify it?

Answer 22

If you want you can write it as:\[\frac{ 1 + 5i }{ 2 } = \frac{ 1 }{ 2 } + \frac{ 5i }{ 2 }\]

Answer 23

but either one is considered correct?

Answer 24

Is the answer different from any of the above?

Answer 25

no? haha

Answer 26

ok i got it, thank you!

Answer 27

you are welcome.