Question

Please help! Will give medal and fan. Thank you in advance :)

1. Simplify the expression. -5 + i/2i

Answer 1

1/i = -i

So i/2i = i/2 * -i = \(\cfrac{-i^2}{2}\)

See that?

Then -5 + i/2i = \(-5+\cfrac{-i^2}{2}\)
Then \(i^2=-1\)

Can you finish it?

Answer 2

Okay. Thank you. I don't think I can honestly, I'm not at all familiar with these problems. I'm very behind in my Algebra class. I don't expect you to give me the answer, but if you could just work with me on it :) that would be great. @ybarrap

Answer 3

You have
$$
-5 +\cfrac{i}{2i}
$$
Right?

Answer 4

Right

Answer 5

I explained that 1/i = -i, which you can use; however you can also cancel the i's:

$$
-5 +\cfrac{\cancel i}{2\cancel i}=-5+\cfrac{1}{2}
$$
See that?

Answer 6

This is the easier approach; however, the 1st approach shows how things work if you play with the imaginary number, i.

BTW, \(i=\sqrt{-1}\) so \(i^2=-1\), just in case

Answer 7

does any of this make any sense?

Answer 8

Okay. So it's easiest to keep the i's in the equation?

Answer 9

Em, I'm trying to grasp it all lol.

Answer 10

yes, if you cancel them, you can just deal with them like regular old numbers

Answer 11

keep trying, it's fulfilling and exciting

Answer 12

Okay. Lol I'm not so sure about it being exciting, so much as complicated.

Answer 13

did I say that, lol

Answer 14

Yes lol

Answer 15

There was a time when people thought that you could not take a square root of a negative number, then someone decided, not that complicated, just make it the letter "i" and deal with it like an ordinary number and see what happens.

Answer 16

Okay.

Answer 17

So once you've simplified you have
$$
-5 + \cfrac{1}{2}=-4\cfrac{1}{2}=-\cfrac{9}{2}
$$

Answer 18

Alright

Answer 19

good luck
\(:-) \)

Answer 20

Thank you @ybarrap

Answer 21

You're welcome