Complex number Definition and 436 Threads

What is d/di(x+iy)?

Homework Statement Write z = 1 + √3i in polar form Homework Equations z = r (cos\varphi + sin\varphii) The Attempt at a Solution Found the modulus by |z| = √4 = 2 Now I am stuck on this part of finding the argument: Tan-1 (√3) now I am not sure how to go from that to...

Homework Statement The mill (single phased) is now affected by a load from a resistor. We assume that the turbine can deliver an infinitely large current without affecting the frequency. figure 1 illustrates the load: http://puu.sh/19GGR The voltage over the capacitor can can be...

Recently, on another forum, the following problem was posted: Given three distinct complex numbers: $\displaystyle z_1,z_2,z_3$ where: $\displaystyle |z_1|=|z_2|=|z_3|\ne0$ and: $\displaystyle z_1+z_2z_3,z_2+z_1z_3,z_3+z_1z_2$ are all real, then prove: $\displaystyle z_1z_2z_3=1$ I...

I am trying to find the z0 to z6 roots of this equation but I am stuck here. Anyone care to show the step by step on how to procced?

Hi, I have a problem with complex number. I do really appreciate your help. I've attempted the question but it's getting me no where. Thanks in advance! Homework Statement Perform the following complex variable calculations, using complex exponentials. Express the results in...

|A>=a|c>+b|d> where a and b are complex numbers. So, is it correct to say that <A|=a^{*}<c|+b^{*}<d| ? Regards.

z is a complex number such that z = \frac{a}{1+i} + \frac{b}{1-3i} where a and b are real. If arg(z) = -\frac{\pi}{2} and |z|= 4, find the values of a and b.I got as far as z = (\frac{a}{2} + \frac{b}{10}) + i(\frac{3b}{10} - \frac{a}{2}) by simplifying the original expression. Then I...

Given that z = 1/(3+it), it is denoted by T on a argand diagram 1. show that z + z* = 6zz* Got this part out but the next part i am totally confused I did abit of loci but i can't figure out this one 2. Show that if t varies T lies on a circle , and state the coordinates of the centre of the...

Hi Everyone. I have been looking at this questions for a while now and have just hit a brick wall. I have found the source impedances using the the following Z of Current source = 1KΩ - jXC =1000 - j4000Ω = 4123<-75.96° Z of Voltage source = 4KΩ + jXL = 4000 + j1000Ω =...

z_1z_2 = -1 + 2i \frac{z_1}{z_2} = \frac{11}{5} + \frac{2}{5}i Given that the origin, z1z2, z1/z2 and z3 are vertices of a rhombus, find z3. I've drawn a sketch on a Argand diagram and the sketch is fine, but to find z3, they have done z1z2 + z1/z2 , but would this not give you a...

Homework Statement Find |exp(√i)|. Homework Equations The Attempt at a Solution I scanned my working as attached, it seems ok to me but I don't understand why it's wrong.. The answer scheme ignores the exp(i sin (pi/4) ) part and writes the answer as exp(cos (pi/4)) =...

Homework Statement α=2e3∏i/4 find α11 in cartesian form. Homework Equations The Attempt at a Solution It's been a while since I've done these but from what remember you add 2kpi to get exp in the range of -∏,∏. so if I let k=15 I get e3∏i/4 but the sltn says it...

Homework Statement Objective: 1. For a two-arm manipulator, use complex-number method to derive the displacement, velocity and acceleration equations for the tracing point P. 2. For a two-arm manipulator, use complex-number method to derive the displacement, velocity and acceleration equations...

If I have a function such that x = - lo{g_2}(x), then must x be a complex number? Thanks.

Homework Statement 43. Let ##w_1, w_2, ... , w_n## be the ##n## distinct ##n##'th roots of unity ##(n\geq0)##. Show that if ##k## is an integer then $$w_1^k+w_2^k+...+w_n^k$$ equals ##0## or ##n##. Find the values of ##k## for which the sum is ##n##. Hint:Write the roots in polar form and...

Homework Statement 37. Let ##z=\frac{i(1+is)}{1-is}## where ##s\epsilon\mathbb{R}##. (a) Show that $$\text{Arg}(z)= \begin{cases} \quad\frac{\pi}{2}+2\arctan s & \qquad \text{for}\quad s\leq1,\\ -\frac{3\pi}{2}+2\arctan s & \qquad\text{for}\quad s>1. \end{cases}$$ Homework...

Homework Statement 4 45^0 Homework Equations The Attempt at a Solution

find all the solutions to z^2+4z ̅+4=0 where z is a complex number.

find all solutions to z^2+4z ̅+4=0 where z is a complex number. Please help with this qn I'm having difficulty. thanks

Homework Statement Hey, I am attempting to fully factorize z^{n}-1=0 for all integers of n where n does not equal zero, and where z is a complex number in the form a+bi. The question asks to first factorize the equation when n=3,4,5. I know how to factorize when n=3 and 4, but I get stuck at...

Homework Statement find the sixth roots of i. Homework Equations The Attempt at a Solution So I started by Arg(z)=pi/2 and |z|=1=r n=6 so z= r^(1/6)*e^i((5kpi)/12) for k=0,1,2...n-1 and that's as far as I got and there answer = e^i*n*pi/12 for n=...

Homework Statement z= 1+i√3 find z^9 Homework Equations The Attempt at a Solution Arg(z) = pi/3 and |z|=2 so z= 2e^i*pi/3 so z^9 = 2^9 (cos6pi +isin 6pi) = 512(1) =512 but the answer has negative 512?

Homework Statement given |z|=3, Arg(z)=5Pi/6 find a+ib form of the complex number. Homework Equations The Attempt at a Solution so from the arg(z) we can say it lies in the second quad. Since 5Pi/6 is equivalent to then 180-150 =30 so, 3(sqrt3/2 +1/2i) but they had...

A complex number is represented by the point P in an Argand diagram. If the real part of the complex number w=\frac{z+1}{z-2i} (z not 2i) is zero, show that the locus of P is a circle and find the radius and centre of the circle. I have a problem manipulating w to find the real part of w

This is probably a silly question, but it is not really clear to me whether De Moivre's theorem of raising a complex number to the nth power only work if n is an integer value? E.g. if I try to raise (2-2i) to the power of 3.01 then my manual calculation get a different result than my...

For some odd reason, I can't think right now. How do I solve $z^4 = -1$ where z is a complex number?

What does it mean if the continuity equation equals a complex number (rather than zero)? I ask this in the context of the probability current.

I would very much appreciate any help with this problem. Homework Statement Find the greatest value of the moduli of the complex numbers z satisfying the equation |z - \frac{4}{z}| = 2 The Attempt at a Solution I tried letting z = a+bi and going from there, but I ended up with this really...

in cartesian form, a+ ib you can find the phase by doing arctan(b/a).. my question concerns the phase of a purely imaginary number. during a lecture my professor said that the phase of i*2pi= pi/2, he rationalized this by saying that the number lies on the y-axis so the angle between the real...

Well I generally haven an idea about subgroup of a group and generators. But I fail to understand following: ({1,-1,i,-i},X) I can see <1>={1} <-1>={-1,1} <i>={i,-1,-i,1} But simply have no idea about <-i> How can you work with -i?

Homework Statement Using Euler's relation, prove that any complex number z=x+yi can be written in the form z= re^{i\theta} where r and \theta are real. Describe the significance of r and \theta with reference to the complex plane. b) Write z= 3+4i in the form z = re^{i\theta} (pretty sure I...

Homework Statement Determine the only real values a, b, c, and d such that the equation: z4+az3+bz2+cz+d = 0 has both z1 and z2 as roots. z1 = 3 + j z2 = -5 + 5j Homework Equations z = x + yj. z = |z|ej\theta The Attempt at a Solution I am not sure where to begin. I can...

If x and y are real quantities what are the solutions for x and y (ix)(1+iy)=(3x+i4)/(x+3y) I have tried grouping the equation into two equal complex numbers but have failed to find a solution which isolates x and y from the two quite long polynomial equations. Does anybody know how to...

Homework Statement z = (n + i)^{2} n is a positive real number, and arg(z) = \frac{\pi}{3} Find the value of n. The attempt at a solution I am reviewing old problem sets from years past, and came across this problem that appears pretty simple. I have my old answer as n=\sqrt{3}...

Hi, Homework Statement Interpret the angle of the complex number (z_{1} - z_{2}) / (z_{1} - z_{3}) in the triangle formed by the points z_{1}, z_{2}, z_{3}. Homework Equations The Attempt at a Solution I'm not entirely sure what to do in this question, I've done a couple of...

Homework Statement cos(4x)(6+2a)+12a+8b=-20 find values for a, b. Then check the values and state which values of x would not have been sufficient checks. Homework Equations Complex number equations The Attempt at a Solution I've simplified it down to this from a harder problem...

e-z2 where z is a complex number a+ib

Homework Statement I have a complex number z=1-i I want to find the argument of this complex number Homework Equations The angle it makes with the positive real axis is arctan(1/1)=pi/4 The Attempt at a Solution This point lies in the fourth quadrant of the argand diagram...

How do you compute the following? 2it where t is a real number while I am at it, how do you compute powers that are not integers ie: 23.14

does complex number have anything like consicutive numbers? . Like 2,3,4 are consicutive integers...

Homework Statement Use de Movire to find solutions for the following: z^5 = i z^4 = i z^3 = i Find generalization for z^n = x+iy, where modulus of x+iy is 1 Explore when |x+iy| is not equal to 1 Homework Equations [rcis(theta)] = (r^n)cis(theta*n) r = /sqrt(y^2 + x^2)...

Hi all. Suppose I am looking for the following quantity: \sphericalangle cn, where cn = \frac{sin(\frac{nπ}{2})}{nπ}. cn is a complex number. According to the book, "Signals and Systems" by Edward Kamen 2nd. Ed., \sphericalangle cn = π for n = 3, 7, 11 ... , and cn = 0, for all other n. The...

(Complex number) I have no idea on this :( Homework Statement If z lies on circle |z|=2, then show that \left\lvert \frac{1}{z^4-4z^2+3} \right\rvert ≤ \frac{1}{3} Homework Equations The Attempt at a Solution Please somebody give me an idea...

Nothing much, I have this: I have studied (myself) about this for many days. And I believe that, for some conditions for a complex ψ,ϕ What are those conditions I mentioned about? And which field of study I should go to see?

Hey, I know the answer to this integral is 2ipi as it was given but I trying to find out how its 2ipi. Here is my working [PLAIN]http://img707.imageshack.us/img707/1681/unledrny.jpg I've been looking at this for ages and I can't work out what I've done wrong thanks,

Homework Statement Suppose that w is a complex number which is not both real and \left\lfloorw\right\rfloor\geq1 (the absolute value of w). Verify that Re[(1-w^{2})^{1/2}+iw]>0. Homework Equations The Attempt at a Solution I attempted to solve this problem by dividing it into...

Hi guys, just before i ask this question i would like to let you know that i am a year 11 student, who has decided to study next years Specialist math (highest level of maths) course early to get a head start as i am nervous for next year(year 12.) :) Homework Statement and The first one...

Homework Statement Express as z = Re[Ae^(i(\varpi t+ \alpha)] 1. z = cos(\varpi t - \pi/3) - cos (\varpit) 2. z= 2sin(\varpi t) + 3 cos (\varpi t) 3. sin(\varpi t ) - 2 cos (\varpi t - \pi/4) + cos (\varpi t) Homework Equations I used cos A + cos B; A = (a2+b2)(1/2); and tan(\theta) = y/xThe...

In general, how many square roots does a complex number have?