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SuperLynx

Member

Registered: 2009-06-28

Posts: 335

complex numbers

I'm trying to understand complex numbers for example 3j or 4i.  I've been reading some sites on complex numbers but still can't wrap my ahead around it's purpose if I have the following formula;

45j + 4 = 49 and so what is the point of j ?

Last edited by SuperLynx (2016-05-15 15:48:13)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: complex numbers

In an equation involving complex numbers, the quantities without j must balance and those with j must balance separately.
If a+bj=c+dj   then a=c and b=d. It is like 2 equations combined into 1. Your equation results in 45=0 and 4=49 which are absurd.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: complex numbers

When do you use complex numbers ?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: complex numbers

Complex numbers have application in electrical circuits and limitedly in mechanics. A complex number can be considered as 2 dimensional vector. vector OA joining  O(0,0) and A (2,3) can be represented by 2+3j. If this is considered as force and a displacement is represented by say 4+2j the product gives work done but only real part of it.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

evene

Member

Registered: 2015-10-18

Posts: 272

Re: complex numbers

Okay, one thing I don't understand: what's the difference between j and i?

I'm used to writing out numbers like this: 49+2i

But here, you guys are using j... What's the difference?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: complex numbers

hi evene

No difference.  There's no absolute authority on which maths symbols to use or even how to spell math.    So you'll find both are used.  It's only the squiggle on the page after all.  It's the square root of minus 1 either way.  Or negative one.  And that could be ee-th er or ahy-th er

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: complex numbers

Hi Superlinx,
usually mathematicians use i and engineers use j . Both mean the same thing. 4+5i is represented by distance 4 along x axis and distance 5 parallel to y axis.You can say an "i" attached with a number rotates the vector by 90^0.
interestingly  4 i^2 means vector 4 along x axis is rotated by 180^0 and becomes -4 . this tallies with the concept that i^2=-1.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: complex numbers

Hi Superlinx,
usually mathematicians use i and engineers use j . Both mean the same thing. 4+5i is represented by distance 4 along x axis and distance 5 parallel to y axis.You can say an "i" attached with a number rotates the vector by 90^0.
interestingly  4 i^2 means vector 4 along x axis is rotated by 180^0 and becomes -4 . this tallies with the concept that i^2=-1.

What if I write a formula 34j, what is that, literally, besides the number 34 ?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: complex numbers

34j is an imaginary number whose magnitude is 34. In an Argand diagram it is represented by a vertical line segment of magnitude 34. You can say j is a unit vector in y direction.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: complex numbers

34j is an imaginary number whose magnitude is 34. In an Argand diagram it is represented by a vertical line segment of magnitude 34. You can say j is a unit vector in y direction.

Why is it only in the Y direction, or it doesn't matter ?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: complex numbers

We represent a complex number in XY plane. real part is along  or parallel to X axis and imaginary part is along or parallel to Y axis.e.g. Let us say you represent a land map as complex plane.say village B is x+jy distance from village A. x is distance along east ( displacement to west considered -ve)and y along north. You can cover the distance by 3 sessions of drive say. a+jb, c+jd, e+jf Then
x+jy=a+jb+c+jd+e+jf
        =(a+c+e)+j(b+d+f)
Real and imaginary parts must separately balance on both sides.
i.e. x=a+c+e  and y=b+d+f  If both are not satisfied you will not reach B.
If there is a village C such that AC=j(x+jy) ,C will be located such that

at the same distance.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

mathisfun_user

Member

From: The Milky Way

Registered: 2016-05-16

Posts: 11

Re: complex numbers

The j is a replacement of the regular i.

j is basically the same as if we were to say i and both indicate (square root negative 1)

I think j's are likely used when performing problems that are in relation to electricity.

j = square root negative 1

i = square root negative 1

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Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers - S. Devi

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality - A. Einstein

SuperLynx

Member

Registered: 2009-06-28

Posts: 335

Re: complex numbers

We represent a complex number in XY plane. real part is along  or parallel to X axis and imaginary part is along or parallel to Y axis.e.g. Let us say you represent a land map as complex plane.say village B is x+jy distance from village A. x is distance along east ( displacement to west considered -ve)and y along north. You can cover the distance by 3 sessions of drive say. a+jb, c+jd, e+jf Then
x+jy=a+jb+c+jd+e+jf
        =(a+c+e)+j(b+d+f)
Real and imaginary parts must separately balance on both sides.
i.e. x=a+c+e  and y=b+d+f  If both are not satisfied you will not reach B.
If there is a village C such that AC=j(x+jy) ,C will be located such that

at the same distance.

You're going to have to give a simpler example, until I can wrap my head around it ?