Argand Definition and 25 Threads

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 the part that requires me to draw the argand diagram. Homework Equations The Attempt at a Solution

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...