Help to study CBSE style.

[ZoraxDoom]

Okay. I am currently trying to study Maths, Chemistry and Physics CBSE style by myself at home.

I'm studying them from IIT Enterance Examination preperation books. The reason for this is that in 2 years, when I'm done with my A levels, I want to give the IIT Enternace examination exams a shot. I won't mind if I don't get in (The odds of me getting in aren't very good anyways), and have other colleges lined up to go to just incase.
So, even if I don't get in, I believe studying these books will be very useful. It will help make my A levels study easier, and will make the transition from A levels to an Engineering college easier too (Since I hear that CBSE kids are more well prepared for Engineering colleges in Maths and Phsycis than O levels / A Levels students.)

Anyways, on topic, I need some help. I'm stuck.

I started with Physics, and must say that MLT system for finding out different Physical Quantities (Dimensional Formulae) is very awesome. So much more useful, and maybe not as simple, but once I get used to this there will be no going back to the old way when it comes to calculating Velocity, Acceleration, Power, etc. Will be more convenient then, and will help in dividing or multiplying different quantities.
Anyways, I got stuck going that as the book brought up Logarithms, something every CBSE student knows and makes every GCSE/IGCSE student go "Huh?".
Now, I could ask for help on that, but chose to start maths and figure it out myself.

I then got stuck on some parts doing Complex numbers (The first chapter for maths).
The chapter itself was easy, but I didn't get some terms, like Conjugate (The Conjugate of Z (Where Z= a + ib) is a - ib). I figured that out, and used it in the further parts, but I'm still a bit unsure. Can someone give me more details on what Conjugate means, and maybe more examples?
I then got to the Geometrical Representation of Complex Numbers. Very cool. But then when it got to Argument of a Complex Number, I got stuck.
I understood it a bit, but what the hell do you mean be The Arguement of a number? I don't get it at all.
There was a paragraph in the book, which said that if the arguement of Z = Alpha, then 2nPie (Where n is an Integer) + Alpha is also an arguement of Z, but the value of Alpha that lies between - Pie < Alpha <= Pie is the Principla Arguement.

I don't fully get this. Can any of the smart people here give me a hand on this, with an example or 2 if possible?

 

[shubhrayu]

I don't like Physics

 

[Kshitiz_Indian]

Okay. I am currently trying to study Maths, Chemistry and Physics CBSE style by myself at home.

I'm studying them from IIT Enterance Examination preperation books. The reason for this is that in 2 years, when I'm done with my A levels, I want to give the IIT Enternace examination exams a shot. I won't mind if I don't get in (The odds of me getting in aren't very good anyways), and have other colleges lined up to go to just incase.
So, even if I don't get in, I believe studying these books will be very useful. It will help make my A levels study easier, and will make the transition from A levels to an Engineering college easier too (Since I hear that CBSE kids are more well prepared for Engineering colleges in Maths and Phsycis than O levels / A Levels students.)

Anyways, on topic, I need some help. I'm stuck.

I started with Physics, and must say that MLT system for finding out different Physical Quantities (Dimensional Formulae) is very awesome. So much more useful, and maybe not as simple, but once I get used to this there will be no going back to the old way when it comes to calculating Velocity, Acceleration, Power, etc. Will be more convenient then, and will help in dividing or multiplying different quantities.
Anyways, I got stuck going that as the book brought up Logarithms, something every CBSE student knows and makes every GCSE/IGCSE student go "Huh?".
Now, I could ask for help on that, but chose to start maths and figure it out myself.

I then got stuck on some parts doing Complex numbers (The first chapter for maths).
The chapter itself was easy, but I didn't get some terms, like Conjugate (The Conjugate of Z (Where Z= a + ib) is a - ib). I figured that out, and used it in the further parts, but I'm still a bit unsure. Can someone give me more details on what Conjugate means, and maybe more examples?
I then got to the Geometrical Representation of Complex Numbers. Very cool. But then when it got to Argument of a Complex Number, I got stuck.
I understood it a bit, but what the hell do you mean be The Arguement of a number? I don't get it at all.
There was a paragraph in the book, which said that if the arguement of Z = Alpha, then 2nPie (Where n is an Integer) + Alpha is also an arguement of Z, but the value of Alpha that lies between - Pie < Alpha <= Pie is the Principla Arguement.

I don't fully get this. Can any of the smart people here give me a hand on this, with an example or 2 if possible?

Well, first things first, which books you're referring to?
Complex numbers, is well, a pretty imaginary kind of concept, which is a bit hard to grasp after all those years of studying real numbers only. Well its just that i is the root of (-1), and therefore since it can't exist its imaginary.

Well in accordance to your last statement about alpha and Pi, I strongly suggest you do trigonometry fully first than complex numbers, because then you would get a strong grasp of radian measure of angles, and would get to know why 2nPi + Alpha is the same as Alpha, or why it should lie between -Pi to Pi(Because its a tan, )

Get on to trigonometry bandwagon first. Also, NCERT books aren't known as the best around, but considering they might help you grasp some concepts, here's a link for them - www.ncert.nic.in , you should be able to find their online books there.

If you still have problems, I'll be glad to solve them!

 

[Harrypotter_fan]

I suppose they are 11/12 CBSE books, right? I might not be much help as I'm in 10th and don't study CBSE.

I know about the MLT system, its just like logic and thats how I used to convert units since um... forever.

About Complex Numbers:
You normally don't leave a denominator complex/imaginary/irrational, etc. So what you do is multiply the fraction with a fraction whose value is 1.
e.g.:
3 / (3 + 2i)
= [3 * (3 - 2i)] / [(3 + 2i) * (3 - 2i)]
= (9 - 6i) / [3^2 - (2i)^2] ... {since, (a + b)(a - b) = a^2 - b^2}
= (9 - 6i) / [9 - (-1)] ... {i = sqrt(-1), so i^2 = -1}
= (9 - 6i) / 10
= (9 / 10) / (3i / 5) ...{ As real and the complex part can't share a common denominator}

I'll be able to help you out with the remaining next year .

 

[ZoraxDoom]

They are IIT preperation books, Tata-Mcgraw Hills. Revision guides basically.

So I'll move onto Trig now, and see if I get it.

 

[Harrypotter_fan]

Hey Kshitiz, can you tell me how to download the online books? I can just view a .pdf index.

 

[Kshitiz_Indian]

Hey Kshitiz, can you tell me how to download the online books? I can just view a .pdf index.

Well its a bit dingy system there. What you do is that you click on the chapter name in the index only (It has to open inside the browser) and then the new chapter will open, and then you save it using the save button, and save each chapter like that.

 

[usy]

I don't like Physics

Physics is life. :cheesy

 

[sohum]

I don't think Shreyas actually concluded his post, which is that a conjugate of a complex number is used to get a real number by multiplying the two together. This is useful when dividing since you can multiply anything by the quantity 1, which happens to be equal to the conjugate over the conjugate.

 

[tassietiger]

I'm getting involved in too many maths discussions lately.

The conjugate is where the imaginary part of the complex number is multiplied by -1. The purpose of this conjugate is mainly as it can get rid of the imaginary part of a complex number. Say you had (3 + 2i) * Z = 13. The only way you could get rid of that 2i is if Z was the conjugate of 3 + 2i, therefore Z = 3 - 2i. Difference of two squares means that (3 + 2i)(3 - 2i) = 9 + 4 (as 2i squared is -4)

The argument of a complex number from memory is the angle it makes when it is put on a coordinate system. If your complex number was 1 + i, it would make a 45 degree angle, a.k.a. pi / 4.

 

[ZoraxDoom]

Wayy too many Tass.

So that's waht a Conjugate is, makes sense.

And yea, when Z = a (Represented on the x axis) + ib (be being represented on the y axis), the Arguement of Z was the Angle made between the line made between the Origin and P (Where the complex number lied on the imaginary plane) and the x axis.

So 1+i would lie on (1, 1) on the graph right? Or rather, (1, i1). Is that the same? Does 1 into the Square Root of 1 = 1? It does make a 45 degree angle if it lied on (1, 1), and I'm assuming that since it is the Imaginary Plane, (1, i1) = (1, 1)

 

[Kshitiz_Indian]

Yeah, 1 + i represents the form x + yi, where x and y are integers, and when plotting only x and y are plotted on their respective axes. So here y = 1 so (1,1) is the point.

 

[Amiya]

I am in 9th reading CBSE... I suggest you to read Mental Ability by Vineesh, it is available for different grades... It's only because of this book that i got 652th All india rank in N.S.T.S.E...

 

[Pranav]

Hey Zorax,I think I might be able to help you.I am in class XI this year & am studying CBSE course.

Lemme tell you about complex numbers.The general form a complex no. is Z=a+ib.
Here 'a' is the real part & 'iota b' is the imaginary part.
When we have to find conjugate of complex no.s we just need to change the sign of the imaginary part of the complex no.

Here are some examples-
*Conjugate of 4+i3 is 4-i3
*Conjugate of 2-i4 is 2+i4

Hope this post was useful.

PranavPathak added 2 Minutes and 21 Seconds later...

So 1+i would lie on (1, 1) on the graph right?

you are right.

Or rather, (1, i1). Is that the same?

yes they are the same.It doesnt make any difference if you right a+ib or a+bi

 

[Neo95]

I am in 9th reading CBSE... I suggest you to read Mental Ability by Vineesh, it is available for different grades... It's only because of this book that i got 652th All india rank in N.S.T.S.E...

You got 652th:cool:.My friend got 79(am not joking).