Question

Simplify the expression.

Answer 1

I believe the answer may be 10i+2/4?

Answer 2

hmm

Answer 3

you can look at it like the sum of two fractions like this..
\[\large \frac{ -5+i }{ 2i }=\frac{ -5 }{ 2i }+\frac{ i }{ 2i }\]

Answer 4

for a simpler form, you want to not have the i 's in the denominator.

Answer 5

So -5i/4? Or would it by 5/4?

Answer 6

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

Answer 7

multiply the first fraction by i / i , the second fraction, the i's cancel from top and bottom

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

Answer 8

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

Answer 9

Wait where did the i/i come from?

Answer 10

it is the same as multiplying something by 1, i/i=1, it is used to get rid of the i in the denominator

Answer 11

@DanJS How did the negatives go away int he second step? At −5i/-2+1/2?

Answer 12

-1/-1 = 1

Answer 13

negative divided by a negative is a positive

Answer 14

@DanJS Ah okay. So 5i/4?

Answer 15

how you get a 4 from the 2

Answer 16

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

Answer 17

@DanJS I was assuming we multiply them? Or do we leave it at 5i/2+1/2?

Answer 18

@DanJS

Answer 19

yeah i would leave it as it is now, in the form a + b*i

Answer 20

@DanJS Alright, thanks for your help! :)

Answer 21

welcome