Complex number Definition and 436 Threads

Homework Statement Hey guys. I have the next transfer function http://img195.imageshack.us/img195/7924/scan0002l.jpg And I want to find the angle of it. I know I can break it into REAL and IMAGINARY but I'm looking for a faster way, is there? Thanks. Homework Equations...

Calculate (-1) ^ i I tried using the formula x^ni = cos (ln (x)^n) + i sin (ln (x)^n) but i cannot solve it. i used MATLAB to get this answer 0.0432139182637723 + 0i but i don't know how to solve it with steps.. can i get some assistance please. thank you.

Can anybody give example of a physical phenomenon which can be stated into a polynomial equation (cubic, quintic or whatever) and which has complex number solutions and those complex numbers have some physical interpretation? The reason for asking such question tagged in physics is that i...

Homework Statement If z = cis @ where @ is acute, determine the modulus and argument of z-1 Homework Equations The Attempt at a Solution As the moudlus of z is 1 z lies on the unit circle. And I can not think of anything more. I drew a graph to see how z-1 seems like in graph...

I was reading Roger Penrose' book "The Road to reality". He mentioned the square root of a+bi in terms of a and b. I am trying to figure his answer out for my self but am struggling. Here goes:(x+yi)^2=a+bi x^2+2xyi-y^2=a+bi x^2-y^2=a 2xy=b I can't rearrange these two equations to get x and...

In the above image the default format of a complex number is taken as a vector, since vector addition is only between 2 similar units (example 10 cos 30 cm + 10 sin 30 cm or 5 cms on y-axis and 2 cm on the x; which gives a resultant following vector addition), it can be said that that the real...

I'm looking at a problem involving complex numbers and a proof. It shows the solution too, but I don't get how they did a certain step. At one step they end up with this: (NOTE: the sigma should have 'n=0' on bottom and infinity on top, but I don't know how to do that in latex. If someone...

Homework Statement Show that the complex conjugation function f:C----->C (whose rule is f(a+bi)=a-bi) is a bijection Homework Equations A function is a bijection if it is both injective and surjective a function is injective if when f(a)=f(b) then a=b a function is surjective if for...

[FONT="Arial Black"][SIZE="7"]SOLVED 1. show that the determinant of a unitary matrix is a complex number of unit modulus 2. i know the equation for a determinant, but i guess to i am not sure what a complex number of unit modulus is either. I'm looking for...

Let z be the complex number: x+iy. Then |z|^2=x^2+y^2 according to my book. But according to the general definition of absolute value, |a|=(a^2)^.5. So letting z=a=x+iy. |z|^2=z^2=x^2+2ixy-y^2 This is not equal to x^2+y^2. I'm confused.

Homework Statement Find the modulus and argument of z=1-cos(a)-i*sin(a) Homework Equations mod(z)=sqrt(a^2+b^2) The Attempt at a Solution mod(z)=sqrt((1-cos(a))^2+(-sin(a))^2) =sqrt(2-2cos(a)) arg(z)=arctan((-sin(a))/(1-cos(a))) This is as far as I can get, I have asked my math...

Homework Statement sketch y=2 under the image w=z^(2) Homework Equations z=x+iy The Attempt at a Solution z=x+(1)i=x+i {y=1 and x can be anything} w=z^(2)=(x+i)^(2)=x^2+2xi-1 after regrouping, w=(x^2-1)+(2x)i and then I consider x^2-1 to be the real part and 2x to...

Homework Statement Hi all. Please take a look at this complex number: \widehat C = \frac{1-\widehat a}{1+\widehat a}\widehat B, where a hat indicates that the number is complex. Can you confirm me in that the length (modulus) of this complex number |\widehat C| is given by: |\widehat C|...

Homework Statement Hi all. Is the phase of a complex number always taken with respect to the real, positive axis? I mean, is it always the direction as shown here: http://theories.toequest.com/content_images/4/argand.gif Thanks in advance.

Hi everybody! I'm trying to find the probability at time t of finding the state pointing in the positive x-direction of an initial system which points in the negative x-direction. I'm not sure if the result is correct, but I get [SIZE="4"]the probability is sin^2(iwt). Can this be understood...

Homework Statement So I've got a polynomial with real roots. It turns out that if you perturb one of the coefficients by a small amount, two of the roots end up in the complex plane. Now I want to find the relative error in my computation. For two real numbers, say x1 and x2, I would take...

http://img353.imageshack.us/img353/672/85253506or3.gif in normal equation i equalize the "Real" part with the real part and the "Im" part with the I am part on the other size of the equation but here there is | | part which makes every thing a^2 + b^2 and it turns everything to...

Hi there, I ve got problem with this equation. x^4+ 14 = 0 I tried like this: X^2 = z z^2 +14 = 0 z^2 = -14 z= sqr-14 z= j 3.74 then back to x x^2 = j.374 and now what can i do??

Homework Statement Equation: \frac{z\theta_0^2}{-\theta^2+ 2i\theta\theta_0\phi+\theta_0^2} Where z, \ \phi are constant and \theta_0 is the initial theta. Find the modulus and the phase associated with this equation. Homework Equations \frac{z\theta_0^2}{-\theta^2+...

Homework Statement 3. Write down the (x+iy) form for the complex numbers with the following modulus and argument (in radians): (a) Modulus 1, argument pi (b) Modulus 3, argument -pi/3 (c)Modulus 7, argument -4 Homework Equations Modulus = ((a)^2 + (b)^2)^1/2 Arg = the angle...

Homework Statement calculate the magnitude of z= i/(6i-3) and the argument of the real and imaginary parts Homework Equations The Attempt at a Solution z=i/6i-3 z*=i/-3+6i? mag(z)=zz* not sure if z* is correct.

Faraday's law is ∫ E dl = - ∂Ф/∂t if we take sqaure root on both sides, √∫ E dl = √- ∂Ф/∂t √∫ E dl = i √ ∂Ф/∂t Now the r.h.s has "i" in it. Does this mean anything? Having "i" in a equation means anything? I have seen "i" in schrodinger equation and dirac equation. As like those...

This is for 10th root unity with complex number multiplication. I am working on closure. I have multiplied 2 elements of my set and I have so far that cos[(n+k)360/10] + isin[(n+k)360/10]. Thus I know that if n+k<=9 then there is an element in the set. Now I need to show for if n+k>9 and if...

Homework Statement Solve z^3 - 3z^2 + 6z - 4 = 0 The Attempt at a Solution I tried factoring a z and quadratic equation but went nowhere Input apreciated

Homework Statement Find an equation connecting x and y for which (z-1)/(z+1) has an argument \alpha Homework Equations z=x+iy arg(z)=tan-1(y/x) The Attempt at a Solution \frac{z-1}{z+1} Substituting z=x+iy \Rightarrow \frac{z-1}{z+1}=\frac{(x-1)+iy}{(x+1)+iy}...

Homework Statement 1)If either |z|=1 or |w|=1,prove that |\frac{z-w}{1-\overline{z}w}|=1 2)If z1,2,3, are complex numbers and \frac{z_2 - z_1}{z_3 -z_1}=\frac{z_1 -z_3}{z_2-z_3} Show that |z2-z1|=|z3-z1|=|z2-z_3| 3) Find the sum of the following series: nC1sinx + nC2 sin2x...

Homework Statement Find the argument of (-2+i)(1+2i). 2. The attempt at a solution z=(-2+i)(1+2i)=-4-3i. I've read on the Internet that I can write z=\rho (\cos \theta +i\sin \theta) where \rho is the modulo of z. I've calculated the modulo of z which is 5. So I have that -4=5\cos \theta...

I was looking around a little bit for an algorithm that would compute a complex number to the nth power. Can anyone supply me a resource that covers this? I wouldn't imagine it being different than some sort of (x+y)^n formula. Thanks in advance.

If I were given a complex number, such as 12/(12+3i) in order to find the real and imaginary parts of the number, I assume that I cannot just reduce the fraction and say the real part is 1 and the imaginary part is 4. I can almost guarantee that this will not calculate the correct answer...

Homework Statement Given the complex number,u, is given by (7+4i)/(3-2i) Express u in the form x+iy Sketch the locus of z such that |z-u|=2 Find the greatest value of arg(z) for points on this locus Homework Equations For z=x+iy |z|=\sqrt{x^2+y^2}...

I am stuck with a complex integration. Integrand looks like this: Exp[-2*pi*i*(Rz+s*z)]. Integration is w.r.t z. Where Rz is function of z, which is little complicated, but for simplicity we can assume z^3. s is just other variable. I was trying to do this integration in Mathematica. If I...

[SOLVED] calculating complex number Homework Statement Calculate {i}^{\frac{3}{4}} Homework Equations The Attempt at a Solution I tried with i=cos\frac{pi}{2}+isin\frac{\pi}{2} i^3=cos\frac{3pi}{2}+isin\frac{3\pi}{2} i^3=-i \sqrt[4]{i^3}=\sqrt[4]{-i} I don't know...

Find z Question: z^3+i=0 My attempt: z^3=-i use z^n=|z|^(n) x e^((i)(n)(theta)) n = 3 |z|=1 theta = -pie/2 Is this correct?

Im trouble getting the correct answer for z^23 where z=1+1 The answer in the back of the book says its 2^16e(i8pie) But z=|z|^(n)e(i(n)theta) Therefore the hypotenuse which is 2^(1/2) when multiplied by 23 should be 2^(23/2) not 2^(16)

(Self-solved) Need help with complex number question Homework Statement I'm looking at this question while practising and I still don't really understand the question entirely. I'm extremely bad with this chapter, not very good at understanding questions and am in need of some help or...

[SOLVED] Representing a wave as a complex number. I'm just a bit confused as to the validity of representing the equation of a wave or oscillatory motion as a complex number. As is my understanding the argument for doing so goes thus: Assuming our amplitude is 1, our equation is: y(t) = cos (...

If I have a function y = if(x), where f(x) is a real valued function, would its derivative be y'=if'(x)...or does something different have to happen with the i part? cheers, W.

Homework Statement Find the real/imaginary parts of sinh(x+yi) and its abs value.Homework Equations The Attempt at a Solution I am able to decompose sinh(x+yi) = cosy*sinh(x) + isin(y)cosh(x) - (which is correct according to my book) Now finding the absolute value is kind of causing some...

Homework Statement Find the locus of the point z satisfying: \left| {\frac{{z - 1 - 2{\bf{i}}}}{{z + 1 + 4{\bf{i}}}}} \right| = 1 2. The attempt at a solution \begin{array}{l} \left| {\frac{{z - 1 - 2{\bf{i}}}}{{z + 1 + 4{\bf{i}}}}} \right| = 1 \\ \left| {\frac{{\left( {x - 1}...

hey, was wondering what would happen if i do : a^b with a : real or complex number and b : a complex number like : 2^i

The phase of a complex number is z=re^{i\theta} This first example is a simple z=1+i, but where does the r come from for this?

Suppose we want to find \int e^x \cos{x} \ dx We know from e^{ix} = \cos{x} + i\sin{x} that the real part of e^{ix} equals \cos{x} . So suppose we want to find that integral, is it ok to study the real part of e^x \cdot e^{ix} ? In that case we get \int e^x \cos{x} \ dx = \int...

Homework Statement Show that: (cosx+isinx)^2= cos2x + isin2x Homework Equations i^2=-1 The Attempt at a Solution Well, here's my attempt! (cosx+isinx)^2=(cosx+isinx)(cosx+isinx) =(cos^2x)+(2[isinxcosx])+(i^2sin^2x) =(cos^2x)+(2[isinxcosx])-sin^2x p.s. when i wrote cos^2x...

not sure if this is in the right section as i havn't got to calculus yet lol. anyways, was wondering whether you could check i have calculated this right as I'm learning complex numbers at the moment and have no way of checking my working. thnx Homework Statement Calculate (\surd5 -...

z^4= 1/2 + i sqrt(3)/2 I start by transforming into polar form: z^4 = e^(i*Pi/3) But then I'm blank.

Homework Statement w=cos(theta) + isin(theta) where 0<theta<pi if the complex number w^2 + (5/w) -2 is purely imaginary, show that 2cos^2 x + 5 cos (theta) -3=0. Hence, find w. Homework Equations cos^2(theta) + sin^2 (theta) = 1 The Attempt at a Solution im guessing to...

w=cos(theta) + isin(theta) where 0<theta<pi if the complex number w^2 + (5/w) -2 = 0 is purely imaginary, show that 2cos^2 x + 5 cos (theta) -3=0. Hence, find w. any input would be appreciated, thx.

In a futile effort to get through Roger Penrose's Road to Reality, I’ve come upon complex number calculus and I have no back round in this topic. So what I am wondering is what do I need to understand before I can do complex number calculus and if there are any good textbooks on this topic.

i added a file in which i tried to solve this question the final equation does"nt come out the question is (z-a)^3=8 it is known that z1*z2*z3=-9 i have dried to make an equation how do i solve this equation?? please help

Homework Statement The question: a)Solve the equation z^{3}=4\sqrt{2}-4\sqrt{2}i.. b)Express the answer in polar form. The Attempt at a Solution Here's what i got: r=\sqrt{\left(4\sqrt{2}\right)^{2}+\left(-4\sqrt{2}\right)^{2}}=8 \tan^{-1}\left(\frac{-4\sqrt{2}}{4\sqrt{2}}\right)=-45^{o}...