Question

What is an interpretation of division by a complex number? It seems like dividing by a vector, which seems sort of weird.

Answer 1

This resource should help you, http://www.regentsprep.org/Regents/math/algtrig/ATO6/multlesson.htm, just reword it.

Answer 2

http://www.regentsprep.org/Regents/math/algtrig/ATO6/multlesson.htm

Answer 3

Either way both of these should help

Answer 4

This source will help you better https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/v/introduction-to-i-and-imaginary-numbers

Answer 5

He wants to know dividing complex numbers not what they represent @ElizabethS

Answer 6

oh lol okay!

Answer 7

Go to this site http://www.cs.berkeley.edu/~vazirani/algorithms/chap2.pdf

Answer 8

@ElizabethS That site you just gave was an excellent resource

Answer 9

Thanks @gamer456148 !

Answer 10

Ugh you win @ElizabethS :)

Answer 11

lol Tanya

Answer 12

Errr I know how to divide by complex numbers, but I just don't see what the significance of it is. Like, what could it mean from a physical standpoint?

For instance, if I have 4 pounds of cake and I divide it into two separate bags, then each person has 2 pounds of cake in a bag. But what about if you have 4 pounds of cake and want to divide it by 2+3i ? What does that even mean to divide by a complex number?

Answer 13

Good description.
@mathslover help him please.

Answer 14

I am dying out of Laughter @tanya123

Answer 15

The significance is you need to know it or you will get an F, now can I get a medal?

Answer 16

Why are you even thinking about it? :P Sometimes, you just have to consider imaginary things.

Answer 17

@mathslover That is what I thought

Answer 18

Like, dividing something *real* by something imaginary, does \(\bf{not}\) make sense in reality, but yeah, maths is all about this.

Answer 19

Well, I've never held the number 2 before. I'm pretty sure all numbers have been imaginary the whole time. There's nothing really that complicated about complex numbers other than they extend the number line into a number plane.

Answer 20

@vishweshshrimali5

Answer 21

Not to be rude or anything but can I please get a medal, it will make me happy?

Answer 22

Nobody has answered my question. Nobody gets a medal lol.

Answer 23

I got a medal :)

Answer 24

lol ... Kainui.. Don't worry. Someone is going to answer your quest. soon.

Answer 25

Kind off unfair, because I am the only one who didn't get a medal lol

Answer 26

Life's not fair. OS is even more unfair. Sorry =P

Answer 27

Okay. Let me see:

Newton's second law of motion says that:

F vector = m * a vector

Right ?

Answer 28

But, I know that I can't divide a vector by another vector

So, how do I get

\(\cfrac{\vec{F}}{\vec{a}} = m\)

Answer 29

@Luigi0210 @agent0smith

Answer 30

Its a very similar case in complex numbers.

Answer 31

Let I have three complex numbers \(z_{1}\), \(z_{2}\), \(z_{3}\)

Answer 32

Give me a medal, seriously somebody gave me a medal then undid it ten seconds later, I wanna make them pissed

Answer 33

Hmm, well in that case they both have the same direction, it's their magnitude that wouldn't divide out. I think it's a good way to think about it.

Answer 34

Such that,

\(\cfrac{z_{1}}{z_{2}} = z_{3}\)

Answer 35

Now take argument both sides

Answer 36

I also know that arg\(\cfrac{a}{b}\) = arg(a) - arg(b)

Answer 37

So. I get

arg(\(z_{1}\)) - arg(\(z_{2}\)) = arg(\(z_{3}\))

Now, what is argument in argand plane ?

Its the angle made by the line joining the point and the origin with the positive direction of real axis or x-axis.

Answer 38

You can represent any complex number as: \[z=r*e^{i \theta}\] so r is the length and theta is the angle part.

But I just don't know if this really works for me very well, since they're just scalar multiples of each other I don't know if I really consider this a very general form of division. I think you're on the right path though, it's getting me to think about it more.

Answer 39

So, it means that difference of two such angles is equal to the angle made by the third and the magnitude of the third one is equal to ratio of the magnitudes of first and second one.

Answer 40

Something like this:



You can clearly understand the magnitude part.