Question

I need a step by step explanation for -5+i/2i
Please help!

Answer 1

are you sure you got that right?

Answer 2

Yes its supposed to be -5+i over 2i

Answer 3

ok so we have an imaginary number as the denominator
We need to convert it to a real number by a multiplication . Also we need to multiply the numerator by this same multiplier.
Does that give you any ideas?

Answer 4

I'm honestly terrible at this. But, I'm guessing that it'd be multiplied by i (Which is -1) I'm seriously not sure of anything beyond that.

Answer 5

yes actually i = square root of -1 so i^2 = -1

this willmake the denominator = -2

now multiply the top by i

Answer 6

2 i * i = 2 i^2 = 2*-1 = -2

Answer 7

Oh, well now I feel like a dork. Is this all I had to do?

Answer 8

I'm assuming not since the top is still left, right?

Answer 9

we have
-5 + i (-5 + i)i
----- = ---------
2i -2

Answer 10

Now you distribute the i over the (-5 + i)

Answer 11

So, -5i +i^2?

Answer 12

right and i^2 = -1

Answer 13

Oh okay so -5i-1

Answer 14

-1 - 5i
-----
-2

Now we can divide the top and bottom by -1 to get rid of the negatives

this gives us (1 + 5i ) / 2

Answer 15

Sorry, I'm trying to write all this down

Answer 16

A complex number is usually written as a + bi The imaginary part comes second.

Answer 17

no problem.

Answer 18

Mkay, so do we have to put (1+5i)/2 into that equation? (a+bi)

Answer 19

Not really though i dont like fractions too much so i would write it as
0.5 + 2.5i which is in the form a + bi

Answer 20

Ah, I get it okay. I don't like fractions either which made this problem even more of a headache.

Answer 21

So would that be the end product?

Answer 22

yes

with these type of problems the way to go is to convert the denominator to a real number
- remembering to multiply the numerator by the same multiplier in order to retain the same value

Answer 23

If the denominator is a complex number you multiply by the Conjugate

for example

1 + i
----
2 + 3i


- multiply by the conjugate of 2 + 3i which is 2 - 3i.

Answer 24

because (2 + 3i)(2 - 3i) = 2^2 + 6i - 6i - 9 i^2

- note that the terms in i cancel out and the value becomes
4 - 9(-1) = 4 + 9 = 13 A real number

Answer 25

Thank you so much for such a detailed explanation! Seriously you've been such a great help!

Answer 26

yw
That's what this site is about.

Answer 27

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