The Argand lamp is a type of oil lamp invented in 1780 by Aimé Argand. Its output is 6 to 10 candelas, brighter than that of earlier lamps. Its more complete combustion of the candle wick and oil than in other lamps required much less frequent trimming of the wick.
In France, the lamp is called "Quinquet", after Antoine-Arnoult Quinquet, a pharmacist in Paris, who used the idea originated by Argand and popularized it in France. Quinquet sometimes is credited with the addition of the glass chimney to the lamp.
Homework Statement :[/B]
Sketch in an argand diagram:
|z − i| = 2
Homework Equations
z= a+bi
The Attempt at a Solution
|z − i| means that the distance from z to i is 2, however I am not sure where to put z.
I've just had my first batch of lectures on complex numbers (a very new idea to me). Algebraic operations and the idea behind conjugates are straightforward enough, as these seem to boil down to vectors.
My problem is sketching. I have trouble defining the real and imaginary parts, and I don't...
hi all,hope I find you all well and that I've posted this in the correct section
ive been given this $z_1$ =1-j2
Question ,find and show the result of $z_1 ^*$ on an argand diagram ,my question is what does the star symbol represent or is it a typo?
many thanks
Homework Statement
What is difference in shading between Argand diagrams containing inequalities with > and ≥ signs?
Example
Shade the appropriate region to satisfy the inequality
|z|> 5
|z|≥ 5
The Attempt at a Solution
I am aware of the fact that both will have circle centered at origin...
Homework Statement
In the argand plane z lies on the line segment joining # z_1 = -3 + 5i # and # z_2 = -5 - 3i # . Find the most suitable answer from the following options .
A) -3∏/4
B) ∏/4
C) 5∏/6
D) ∏/6
2. MY ATTEMPT AT THE SOLUTION
We get two points ( -3 , 5 ) & ( -5 , -3 ) => The...
Homework Statement
OABC is a square on an Argand diagram. O Represents 0, A represents -4 + 2i, B Represents z, C represents w and D is the point where the diagonals of the square meet. (There are two possible squares that meet this criteria) Find the complex number represented by C and D in...
Hi all, I'm hoping for some help/guidance on this problem:
1. Homework Statement
The complex number z is represented by the point P on the Argand diagram. Sketch and describe in words the locus of P if:
i) ##|2-iz|=2##
ii) ##|\dfrac{1+i}{z}-2|=2##
The solutions read:
i) ##|2-iz|=2...
Homework Statement
Find the locus of points which satisfy
2π*|z −1| = Arg(z − 1) where |z −1| ≤ 2.
Homework Equations
n/a
The Attempt at a Solution
I know that |z-1| ≤ 2 is the 'inside' bits of a circle center (1,0) with a radius 2
After that I get confused surely with |z-1|≤2 then...
I am wondering how one would go about drawing graphs in Argand plane using Wolfram Alpha. For instance, I want to plot an ellipse $|z-1|+|z+1|=5$ using W|A, what should be the input? Simply entering $|z-1|+|z+1|=5$ doesn't give what I want.
Thanks!
Homework Statement
Sketch the locus of points in the argand diagram defined by z:
arg (z-1) - arg(z+1) = ∏/4
Homework Equations
The Attempt at a Solution
By simple geometry i worked out that at a point in the x-y plane, the angle subtended from that point to -1 and 1 must...
Homework Statement
The potential difference across a circuit is given by the complex number
V=40+j35volts
and the current is given by the complex number
I=6+j3 amps
a) sketch the appropriate phasors on an Argand diagram.
b) Find the phase difference between the phasors for voltage V and...
1. Question
Note: arg ( ) refers to the argument of the complex number, i.e. the angle. | | refers to the modulus, the length.
Since I don't know how to show an Argand diagram here, I will describe my solution algebraically.1. (a)
arg(z - 3) = -3∏/4, arg(z + 3) = -∏/2
1. (b)
arg(z - 4i) =...
I'm having trouble with the various geometrical representation of complex numbers.
Can someone provide me link where this is discussed, or maybe an argand plane graphing calculator online?
Homework Statement
Plot 3e^(-i5∏/3) on an Argand Diagram
The Attempt at a Solution
Re(e^iθ) = cosθ = cos(-5∏/3) = 1/2
Im(e^iθ) = sinθ = sin(-5∏/3) = √3 / 2
So I'd go along the x-axis to 1/2 and then upwards in the y-direction to √3 / 2 and plot the point there.
Is this the...
Homework Statement
draw an argand diagram of the complex voltage v at t=pi/1800, also how do i obtain the instantaneous voltage
Homework Equations
i = lcoswt
The Attempt at a Solution
well so far i have a straight line
Homework Statement
Given that arg(z/(1-i))=pi/2, find the argument of z.
Sketch , in the Argand diagram , the set of points representing z and the point representing the complex number w=-4+3i. Hence deduce the least value of |z+4-3i|
Homework Equations
The Attempt at a Solution...
Hi just did an interesting question which made me wonder about solving it another way around
z = 2 + 5i
find the value of [/tex]z^{\frac{1}{4}}[/tex] which lies in the second quadrant of the Argand diagram and enter it's argument
So arctan(5/2) \approx 1.1902
We use De Moivre's...
Homework Statement
Draw an argand diagram to represent the follwing property:
real(z) < abs(z) < real(z)+img(z)
Homework Equations
z = x+iy;
real(z) = x
abs(z) = sqrt(x^2 + y^2)
img(z) = y
The Attempt at a Solution
substituting original expression with x, y, and sqrt(x^2 + y^2)...
Homework Statement
I'm looking at bii) of the question.
Its my very first attempt at argand diagram and i do not really know how to construct one.
Homework Equations
The Attempt at a Solution
Homework Statement
(z^3)-1 = 0. Solve the equation and show that the roots are represented in an Argand Diagram by the vertices of an equilateral triangle.Homework Equations
The Attempt at a Solution
i can only found 1 as the answer.By transferring the -1 to the other side to become 1 and cube...
For this I started with the 1st interval [0,pi/2] and said
arctan [4/ ... ] = [0 , pi/2]
but studying the tan graph this is all positive values of the y-axis
so surely the range of values for this is (0 , inf)?
If I've done that right, how do I do the other interval [-pi/2 , pi]...
http://img513.imageshack.us/img513/3874/85311748.th.jpg
Can someone please ler me know how to go about this problem? I have made z the subject, however do not know how to advance.
Thanks
On an Argand diagram, sketch the region R where the following inequalities are satisfied:
l iz + 1 + 3i l less than or equal to 3
How do you draw this loci?
Do i manipulate the equation?
if so i got this :
l z - ( -3 + i ) l less than or equal to 3i
But how in the world do you draw this...
Homework Statement
If w=costheta + i sintheta and theta is between -pi and pi: Find theta if E O and A are on the same straight line. E is a point on diagram representing w(z3).
Homework Equations
The Attempt at a Solution
Ive found the following:
z1 (1+(sqrt3)i)
z2...