Question

How do you simplify -5+i/2i

Answer 1

5i/2i?

Answer 2

2i^2? (I suck at math so...)

Answer 3

yes. and i^2 is special.... it also means -1

Answer 4

So all in all it's 5i/2i^2?

Answer 5

the bottom 2i^2 which can be rewritten as 2* -1= -2

the top is (-5+i)* i which can be simplified (distribute the i)

Answer 6

-6 right?

Answer 7

or actually 6

Answer 8

i*(-5+i) is done the same way as

x(a+b) = ax+bx

you should get i*-5 + i*i
can you simplify that?

Answer 9

4?

Answer 10

you can't ignore the i, it has to stay ....

Answer 11

*5

Answer 12

oh then its 6i? (-1)-1=1 and -5(-1)=5 and 5+1=6i

Answer 13

So 6i/-2i

Answer 14

let's start at the beginning
\[ \frac{ (-5+i)}{2i} \]
people don't like i in the denominator. so multiply top and bottom by i
\[ \frac{ (-5+i)}{2i} \cdot\frac{i}{i}\]
what is the bottom? (what is 2*i*i ?)

Answer 15

2

Answer 16

almost. remember i*i is -1
try again

Answer 17

2*-1=-2. -2*-1=2. and -1*-1=1, 2*1=2.

Answer 18

all of that is true.

but what is 2*i*i ?

Answer 19

the way you do it is bit by bit
2*i*i is 2 * (i*i)
replace i*i with -1
2 * -1
replace 2*-1 with
-2

so the bottom is -2

Answer 20

you now have (after replace 2*i*i with -2)
\[ \frac{ (-5+i)i}{-2} \]

Answer 21

But wouldn't i*i=-1*-1 is i=-1

Answer 22

i*i= -1
end of story

Answer 23

alright and we can solve the numerator normally?

Answer 24

i is sqrt(-1)

and sqrt(-1) * sqrt(-1) is -1
just remember
i*i= -1

Answer 25

now for the numberator.
first step is "distribute" the i
can you do that?

Answer 26

Not sure how I would.

Answer 27

distribute is a rule you should learn

here is the rule with numbers (not letters)
2*(3+4)
we know this is 2*7 (right?) = 14
notice that we can do this
2*3 +2*4
6+8
14

here is the rule with letters:

x*(a+b)
x*a + b*x

you multiply the "thing" on the outside times each thing on the inside

try it with

i * (-5 + i)

Answer 28

So its i*i+i*-5?

Answer 29

yes. so now we have

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

now can you replace i*i?

Answer 30

-1+5 right?

Answer 31

i*i is -1
but you don't drop i from -5*i
so far we have
\[ \frac{-1 +i*-5}{-2} \]

Answer 32

to make it look nicer we don't have to write the * (for multiply)
we can just write -5i (which means -5*i which is the same as i*-5 , you can swap order when multiplying)

so we now have
\[ \frac{-1 -5i}{-2} \]

I would multiply top and bottom by -1
can you do that ?

Answer 33

5i/2?

Answer 34

you did the bottom correctly

now re-do the top:
-1*(-1-5i)

remember the "distributive law" (see up above where we used it)

Answer 35

So 6i? -1*-1+-5*-1?

Answer 36

-1*-1+-5*-1? is almost correct except I don't see i in there

Answer 37

Yea sorry, was called away. But thanks.

Answer 38

you are almost done here.
-1*(-1-5i)
you multiply the "thing" on the outside times each thing on the inside

(and remember to keep the i.