Complex number Definition and 438 Threads

  1. G

    Evaluating Im (z*w)/(2z-3w) for z=3-i and w=1+3i

    hey guys I've got a problem If z = 3− i and w = 1+3i, evaluate Im (z∗w)/(2z − 3w) my attempt... ill do top first (3+i)(1+3i)=3+9i+i+3i^2=10i? bottom=3-2i-3+9i=7i therefore answer equals 10/7 however answer is 3/13. could someone please help. thanks
  2. A

    Finding the Angle of a Complex Number: Tips and Tricks

    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...
  3. A

    How Do You Compute (-1)^i in MATLAB?

    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.
  4. sujoykroy

    Physical phenomena with complex number solution

    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...
  5. 3

    Calculating Modulus and Argument of a Complex Number | Homework Question

    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...
  6. G

    Finding the square root of a+bi (complex number)

    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...
  7. D

    Representing complex number as a vector.

    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...
  8. P

    Understanding Complex Numbers and Their Proof: A Step-by-Step Explanation

    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...
  9. D

    Bijection in a complex number ring

    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...
  10. S

    Proving Determinant of Unitary Matrix is Complex Number of Unit Modulus

    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 guidance
  11. T

    Confused about the absolute value of a complex number

    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.
  12. C

    Finding modulus and argument of a complex number

    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...
  13. T

    Graphing the image of a complex number

    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...
  14. N

    Finding length of a complex number

    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|...
  15. N

    Is the Phase of a Complex Number Always Taken with Respect to the Real Axis?

    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.
  16. C

    Interpretation of probability which includes complex number

    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 the probability is sin^2(iwt). Can this be understood as the...
  17. P

    Relative error between a real and complex number.

    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...
  18. T

    How Do You Solve Complex Equations Involving Absolute Values?

    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...
  19. G

    How can I solve the complex number equation x^4 + 14 = 0?

    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??
  20. A

    Complex Number (Modulus/Phase)

    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+...
  21. C

    Simple complex number question

    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...
  22. B

    How Do You Calculate the Magnitude and Argument of a Complex Number?

    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.
  23. S

    Faraday's law and complex number

    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...
  24. B

    C10 Group, 10th roots unity with complex number multiplication

    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...
  25. C

    Stuck on Complex Equations: Can You Help?

    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
  26. R

    Checking the answer to complex number question

    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}...
  27. R

    Couple of complex number questions

    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...
  28. fluidistic

    Find the argument of a complex number

    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...
  29. M

    Raising a complex number to the nth power

    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.
  30. M

    Finding Real and Imaginary Parts of Complex Numbers

    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...
  31. R

    Greatest value of the arg. of a complex number

    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}...
  32. G

    How can I numerically integrate a complex function with Mathematica?

    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...
  33. T

    How Do You Calculate the Fourth Root of i Cubed?

    [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...
  34. R

    Solving Complex Number Question z^3+i=0 using z^n=|z|^(n) x e^((i)(n)(theta))

    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?
  35. R

    Complex Number Exponentiation: Finding the Power of z^23 for z = 1+1

    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)
  36. P

    How Do You Solve a Complex Number Problem Involving a Parallelogram?

    (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...
  37. F

    Representing a wave as a complex number.

    [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 (...
  38. W

    Does the i Part Affect the Derivative of a Complex Number Function?

    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.
  39. J

    Absolute value of a complex number

    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...
  40. U

    Complex Number Locus: Find Locus of z

    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}...
  41. J

    Exploring the Result of a^b with a Real or Complex Number

    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
  42. O

    Understanding the Complex Number r in z=re^{i\theta}

    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?
  43. X

    Is There a Trick to Simplifying Integrals of Complex Numbers?

    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...
  44. N

    Proving (cosx+isinx)^2: A Simple Complex Number Problem | Homework Solution

    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...
  45. T

    Calculating Powers of Complex Numbers: Is My Answer Correct?

    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 -...
  46. K

    What is the Argument of a Complex Number with a Given Modulus?

    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.
  47. A

    Solving Complex Number Proof: w^2 + (5/w) - 2 = 0

    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...
  48. A

    Proof: Complex Number w^2+(5/w)-2=0 is Purely Imaginary

    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.
  49. H

    What do I need to know before studying complex number calculus?

    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.
  50. T

    How do I solve (z-a)^3 = 8 when z1*z2*z3 = -9?

    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
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