MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 2,200 off
USE CODE: chait6

				   

complex nos have an analogy with points on cartesian coordiantes.


So how it is that (x,y) gets converted into x+iy.


i know all those derivations that i*y gives complex no.(A point on y axis), but why the plus sign in between intead of ",". what is its significance. Is it adding of complex no. to real no.(makes no sense) or anything else, why not minus"-"?

7 years ago

Share

Answers : (1)

										

Hi twesh,


A complex number can be viewed as a point or "Position Vector" in "a" two-dimensional Cartesian Coordinate "system" called the "Complex Plane" or Argand diagram. Here the point to note is :




The Argand Plane is a    """"2D Cartesian Coordinate System"""" that has been created , in order to conduct operations on complex numbers graphically.


Now (x,y) is coordinate of a point in a "2D Cartesian Coordinate System" that has x- and y- axes both of real numbers.


Now to visualise Complex Number Operations Graphically, we create another "2D Cartesian Coordinate System", that has x-axes as the real numbered axes, and y-axes as the imaginary numbered axes,


Hence the coordinates of any point on this plane, in this system, "called the Argand Plane", the co-ordinates of a point are not(x,y) BUT (x,iy)


"the real axis and the orthogonal imaginary axis"


Complex Plane is "a modified Cartesian Plane"


And another characteristic that we, the creators of this Argand plane, assign to this Plane is that Position "vectors" are not (x)i + (iy)j


BUT "x+iy".


=======================


In this Case, Remember that : First we had the complex numbers 2+3i


And Then,


We created the Argand Plane(a 2D Cartesian System) to visualise their opeations like additions and multiplication, etc.


While creating this Argand Plane, we assigned it a few characteristics that were needed in relation to complex numbers.


 


-----------------------------


The Definition:


The concept of the complex plane allows a geometric Interpretation of Complex Numbers. Under addition, they add like Vectors. The multiplication of two complex numbers can be expressed most easily in polar Coordinates – the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as a rotation.


 


Regards,


Rajat


Askiitians Expert

7 years ago

Post Your Answer

Other Related Questions on Algebra

If alpha is a real root of the equation ax 2 +bx+c and beta is a real root of equation -ax 2 +bx+c. Show that there exists a root gama of the equation (a/2)x 2 +bx+c which lies between alpha...
 
 
 
Ajay 6 months ago
 
Small Mistake in last para posting again..............................................................................................................
 
Ajay 6 months ago
 
We have Similarly, So if P(x) = a/2 x 2 +bx +c, then and are off opposite sign and hence there must exist a root between the two numbers.
 
mycroft holmes 6 months ago
In the listed image can you tell me how beta*gamma = 2 ….. . . .. ??
 
 
The value of gamma is still not correct, either printing mistake or you gave me wrong value. The correct value of gamma is below
 
Ajay 5 months ago
 
Thankyou so much............................. …......................................................................!
 
Anshuman Mohanty 5 months ago
 
Yes sorry..... . . . .it is not so clear.. ok the values are beta = α + α^2 + α^4 and gamma = α^3 + α^5 + α^7
 
Anshuman Mohanty 5 months ago
if |z - i| Options: a*) 14 b) 2 c) 28 d) None of the above
 
 
If |z-i| = ?? PLs complete the question
  img
Nishant Vora one month ago
 
Got it! [z + 12 – 6 i ] can be rewritten as [ z – i + 12 – 5 i] => | z – i | and => |12 – 5 i | = sqrt ( 12^2 + 5^2) = 13......................(2) => | z + 12 – 6 i | => | z + 12 – 6 i |...
 
Divya one month ago
 
I tried posting the question several times, it kept cutting off the rest of the question. Here: If | z-1| Options: a*) 14 b) 2 c) 28 d) None of the above
 
Divya one month ago
sin^2 6°-sin^2 12°+sin^2 18°-sin^2 24°......15 solve it Urgent
 
 
Ajay, the complete qution isSolution is sin^2 6°-sin^2 12°+sin^2 18°-sin^2 24°..... upto 15 terms. sin 78°=0 sin 42°+sin 54°+ sin 66°+ + sin 18° sin 6°+ where )=0.5 (your required answer),...
 
Kumar 3 months ago
 
Not any people get my answer why. You can no give answer my question I am join this site
 
Vivek kumar 5 months ago
 
Hello If you want to get the solution quick you should post your question in clear manner. Its not clear what you wnat us to solve, and what does 15 at the end of question means?
 
Ajay 5 months ago
Solve: (sin theta+cosec theta)^2 + (cos theta +sec theta)^2- (tan^2 theta + cot ^2 theta)^2
 
 
What needs to be solved here ? The question is incomplete....................................................................
 
Ajay 6 months ago
 
i don’t know how to do this...............................................................................................
 
Saravanan 2 months ago
 
this is the question :: Solve: (sin theta+cosec theta)^2 + (cos theta +sec theta)^2 - (tan^2 theta + cot ^2 theta)
 
Naveen Shankar 6 months ago
solutions to Question no. 17,18 19 and 20 pleaseeeeeeeeeee
 
 
Let the feet of the altitudes on BC, AC, AB, be D,E,F resp. Let the orthocenter be H. The following can be proved easily: ​1. HDCE and HFBD are cyclic quadrilaterals. Then chord HE subtends...
 
mycroft holmes one month ago
 
Draw which is Isoceles as OB = OC. Now which means . Let D, be the foot of the perp from O on BC ( which is also the midpoint of BC). Then OD = OC sin (OBC) = R cos A. Hence the required...
 
mycroft holmes one month ago
 
a cos A = b cos B 2R sin A cos A = 2R sin B cos B sin 2A = sin 2B Either A = B (isoceles or equilateral) or 2A = 180 o – 2B so that A+B = 90 o .(Right-angled)
 
mycroft holmes one month ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 6,000 off
USE CODE: chait6

Get extra R 2,200 off
USE CODE: chait6

More Questions On Algebra

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details