9that means u shud strenghthen ur coordinate geo , once done that complex bcums easier
I'm having trouble with complex numbers.[2]
My friends say "Machan, that's one of the easier topics to score in JEE". So I want to improve in that area. Please suggest a few tips for that.
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15 Answers
62Tips:
Think of complex number as a number on a plane.. (x-y) plane
if you can get this much then you have done half the work!!
It is indeed one of the simpler topics!
11I did think of it that way, bhaiyyah. But after I did that, probs seemed to get twice as tough as they were before[2]
911Seeing eqns in x and y is a whole lot easier than z and z [1]
11If z is a point on the argand plane, what should I imagine z as? [12]
62its mirror image on the y axis..
but then knowing just the argand plane does nto help.. you have to make sure that you know the other stuff as well
do some practice and you will be upto this challenge :)
106nishant bhaiyya cud u show me some applications of coordinate geometry in terms of complex numbers. This is one part that I have not understud.
62ashish... try to solve these very basic problems..
What is the number of solution of
|Z|=5 and Re(Z)=Im(Z)
106there are two solutions.
mod(z) = 5 means z lies on a circle of radius 5
no Re(z) = Im(z) ==> z is in 1st of 3rd quad and vector joining z makes angle 45
So, z is + - (5 + 5i)
Nishant bhaiyya i am asking about the use of straight line equation, circle equation andall
62what is
kZ when k varies from -infinity to infinity
what is
kZ+Z1 when k varies from -infinty to infinty
62what will z.k be for a fixed z belonging to complex numbers...
and for k varying from -infinity to infinity?
106it will be a straight line i.e the line joining origin and z
But i m asking about the equations i.e the one using z and z(conjugate)
62ashish i understand that you know enuf of what i am trying to say.. but could you yourself give some question.. so that i can see if we can apply geometry or not...
You will appreciate that geometry cant replace complex numbers..
but it can infact make things easier a lot of time....
You have to know how to fall back to the originial standard methods if geometry does not work!
106like a.z(conjugate) + a(conjugate).z + b = 0 represents a straight line.
How is this used to solve problems.
62umm...
well ashish to be true i dont have enuf understanding of this one when it comes to converting this equation to a geometry problem...
I am bookmarking it for my future reference....
whenever i am able to think about it.. i will post the method to you directly...
right now i dont have a method! But i am sure there must be some physical interpretation of the same as well....