# What is Argand: Definition and 25 Discussions

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.

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### How can I sketch the following in an Argand Diagram?

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.
2. ### I Sketching Complex Numbers in the Complex Plane

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...
3. ### MHB Solving for $z_1^*$: Argand Diagram

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
4. ### Shading in Argand diagrams involving inequalities

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...
5. ### Argument of a random complex no. lying on given line segment.

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...
6. ### Complex numbers - I'm sure this is an easy - Argand diagram

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...
7. ### Help with complex loci on Argand diagram

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...
8. ### Exploring the Locus of Points in an Argand Diagram

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...
9. ### MHB Plotting complex equations on the Argand plane with Wolfram Alpha

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!
10. ### Argand Diagram: Difference in argument = pi/4

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...
11. ### Argand diagram, phase difference & power

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...
12. ### Using an Argand diagram, find the solution satisfying these pairs of equations

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) =...
13. ### Can someone help with Argand plane graphing and finding the radius?

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?
14. ### Plotting Complex Numbers on an Argand Diagram

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...
15. ### Drawing an argand diagram of complex voltage

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
16. ### Solving Argand Diagram: Finding z + w = -4+3i

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...
17. ### Getting the argand with De Moires theorem

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...
18. ### Representation of properties of Complex Numbers in Argand Diagrams

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)...
19. ### Drawing an Argand Diagram: 2 Homework Statement

Homework Statement I'm looking at the part that requires me to draw the argand diagram. Homework Equations The Attempt at a Solution
20. ### Constructing an Argand Diagram - My First Attempt

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
21. ### Complex Numbers using Argand Diagram

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...
22. ### Solving Argand Diagram for [0,pi/2] & [-pi/2,pi] Intervals

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]...