Complex numbers Definition and 724 Threads

Homework Statement z1 = 1 + i, z2 = i − 5 are points in the complex plane. If z2 is rotated about z1 by 450 find its new position. Attempt at solution Absolutely no idea! I think I might need to use e^theta*i but not sure!

I was trying to think how to introduce complex numbers in a more natural way. I find defining \mathrm{i}=\sqrt{-1} just to not get stuck in maths and then be surprised by the power of complex numbers unsatisfactory. There are probably other ways, but they are abstract, too? Here is some visual...

Homework Statement For a cubic polynomial P(x), with real coefficients, P(2+i)=0, P(1)=0 and P(0)=10. Express P(x) in the form P(x)=ax^3+bx^2+cx+d and solve the equation P(x)=0 Homework Equations The conjugate factor theorem The Attempt at a Solution Using remainder...

Homework Statement Using only the axioms for a field, give a formal proof for the following: a) 1/z1z2 = 1/z1 1/z2 b) 1/z1 + 1/z2 = z1 + z2/z1z2 The Attempt at a Solution I really am having a tough time understanding this problem. I know the axioms of a field i.e...

Can anyone please provide me 3 examples where complex numbers are used in kinematics.

I hope, I've posted this question in the right section. Homework Statement Solve the fooling equation over C z^3+ 8 = 0 The Attempt at a Solution First Attempt z^3 = -8 cube root (2 ^3) = cube root (8 i^2 ) z = 2i Second Attempt z^3 = -8 z ^3 = -2 ^3 so, z = -2

My aim is to interpret two-dimension vector quotients. I will be using this as the analogue to what a quaternion is. Ok here goes: *only considering vectors in two-dimensions* We define a vector to be a directed line from A to B. We define equality between two vectors if we can use...

Let U=a+jb, V=c+jd. What is U X V? Where "X" is the cross product. Can you explain?

What is the difference between Complex Numbers in polar form as opposed to rectangular form?

Homework Statement x³ - 64 = 0 Find the complex roots of this, giving your answers in the form of a + ib where a and b are real Homework Equations The Attempt at a Solution well the cube root of 64 is 4, and that's real. I don't see how there can be any imaginery numbers here. 4 x4...

I have a very simple question, but have been unable to find an answer for it. When using fortran 90 can you use a DO loop to calculate a complex number? For example: [code] COMPLEX FUNCTION forwards (tincdum,tstartdum,tenddum,fdum,ydum,idum,wdum&...

x3+4x2+9x+10 finding 1 root and using synthetic division we can factorize to: (x+2)(x2+2x+5) using complex numbers to factorize (x2+2x+5) we have (x+1)(x-2i)(x+2i), and so our final solution is: (x+2)(x+1)(x-2i)(x+2i) is this correct?

i have just started on complex numbers today and have read that the "algebraic rules for complex are the same ordinary rules for real numbers".. when multiplying 2 complex numbers (z1 and z2) i can see easily that: (x1+y1i)(x2+y2i) = x1x2 + y1x2i + x1y2i +y1iy2i however I am struggling to...

Homework Statement z+(conjugate of z)^2=4 Homework Equations z = x+iy (x+iy)+(x-iy)^2=4 The Attempt at a Solution the solutions give (x+iy)+(x-iy)^2= x + x^2 - y^2. how do they reach that? I get (x+iy)+(x-iy)^2 = x + iy + x^2 -2xiy + i^2*y^2. I think the question is the (...

Homework Statement Hi all. When finding the argument of a complex number using tan(\theta) = y/x (where z = x + iy), sometimes I do not get the correct answer. I assume this is because tangent is only defined for -pi/2 to pi/2 (and from this it is periodic). So is it a good idea always...

Homework Statement Two "waves", characterized by cosx and cos^2(x/2) interfere. Using phasors or complex numbers or trigonometry as necessary, aggregate "cosx + 2cos^2(x/2)" - i.e. rewrite as a single cosine. Homework Equations I was told that there is an error in the way this questions...

hello I am working on a book on maths and i have come to a part i need help with. (7-j4)(4-j3) is the equation i know that a^2-2ab+b^2 but what is the formula for abcd the answer i have to get to is 28-j37-12 from what i know allready i got the 28 and the 12 so if you can help or...

What changes to the algebraic rules when imaginary "i" is introduced in addition to real numbers? I know that complex numbers do not have a "<" or ">" relation. Some functions become multivalued. What about school algebra? Maybe exponentiation rules are slightly modified?

Homework Statement ive been given this system of equations and told to solve it: x+2y+2z=-3 2x+y+z=0 x-y-iz=i Homework Equations all elementary row operations The Attempt at a Solution 1 2 2|-3 2 1 1| 0 row2-row1 then row2 x -1/3 1-1-i| i 1 2 2|-3 0 1 1|-2 row3-row1...

Homework Statement how do i find the roots of this: x^2-(2-1)x+(3-i)=0 Homework Equations -b+-sqrtb^2-4ac/2a (quardaric equation) The Attempt at a Solution

Hey guys. So, complex numbers. Its been a while since I've dealt with them. I've been wondering a few things about them. When expressed in the form a + ib, is there a particular way that you square them? And when you have a rational number, with an i term on the bottom, how exactly...

Hi, I am currently studying complex numbers and I am at the part we have to find line integrals over a simple closed curve gamma(t).. I know the definition, but when i read a problem I am n ot sure how to parameratize the curve. I was wondering if there are some tricks to this. Would...

Hi, I am currently studying complex numbers and I am at the part we have to find line integrals over a simple closed curve gamma(t).. I know the definition, but when i read a problem I am n ot sure how to parameratize the curve. I was wondering if there are some tricks to this. Would...

Hi. I have recently scratched the basics of complex numbers and just learned the modulus. I looked at one of the examples on my textbook which states that l (-1+ 31/2i)l = ((-1)2+(30.5)2)1/2 But according to my understanding, isn't the l31/2il supposed to be sqrt of 3i2, in which it is a...

Homework Statement The system of equations: ix - y + 2z = 7 2x + αz = 9 -x + 2y + 5iz = β has a unique solution, except for one value of α. What is this α - value? If the matrix doesn't have a unique solution, then what value should β have for the matrix to be consistent and what is...

Homework Statement \int x* exp(-\alpha x -ikx)dx the integration is definite with limits (x: 0---->inf) alpha , k are real constants 2. The attempt at a solution I used integration by parts and arrived at the result \frac{xexp(-\alpha x-ikx)}{\alpha+ik} +...

Homework Statement If z is a non-real complex number such that z+1/z=2costheta, prove that z^n+1/z^n=2cosntheta for any posistive integer n Homework Equations I think the process of induction would work, but I am not quite sure how to do that with all of the unknowns, would i just treat...

Homework Statement The angles \theta and \phi lie on the interval (-pi/2,pi,2) and z=(cos\theta +cos\phi)+i(sin\theta +sin\phi) Show that |z|=2cos(\frac{\theta - \phi}{2}) and find arg(z) Homework Equations If z=x+iy |z|=\sqrt{x^2 +y^2} The Attempt at a Solution |z|=...

Homework Statement Trying to write -8\pi - 8\pi\sqrt3 j in exponential I got the coefficient as 16 pi but to get the theta in top of the exponential I have to do the inverse tangent of \frac{-8\pi} {-8\pi\sqrt3 j} I know it is pi over 3, but what is the easiest...

Homework Statement Describe the set of points z in the complex plane that satisfies each of the following. |z|=3|z-1| x^2+y^2= 3[(x-1)^2+y^2] x^2+y^2= 3[x^2-2x+1+y^2] x^2+y^2= 3x^2-6x+3+3y^2 -2y^2= 2x^2-6x+3 -y^2= x^2-3x+\frac32 -\frac32-y^2=x(x-3)...

Is there any way to use the FindFit function with complex data/functions, but to only return real results for the parameters? Right now I'm getting the following error: FindFit::nrnum: The function value 62.6185+25.5493i is not a real number at {c1f,c2f} = {1.,1.}. From the code...

Homework Statement Integrate using complex numbers \int\limits_0^{2\pi} cos^4(\theta) Homework Equations cos^4(\theta)= (\frac{e^{j\theta} + e^{-j\theta}}2)^4 The Attempt at a Solution \frac 1{2^4} (e^{j\theta} + e^{-j\theta})^4 I got \frac 1{2^4} \int^{2\pi}_0...

Homework Statement I was looking up complex numbers and the guy on YouTube made something similar to this equation: i=-1 c^2-(d^2*i^2) = c^2+d^2 ( - 2:55) Homework Equations I do not understand why it is "c^2+d^2" and not "c^2-d^2" I would like a detailed explanation, as I might have...

I had a question on a test...and I am trying to figure what is wrong...it seems easy...so what am i missing? What is the phase angle, in degrees, when you divide 62 at an angle of 97 degrees by 18 at an angle of 52 degrees? I came up with 45...but the answer said 79? I thought all you...

Homework Statement I've never understood e^{i\theta} very well. I know that e^{i\theta} = cos \theta + i sin \theta, but how about e^{4i}? Would this be cos 1 + 4i sin 1 or cos 4 + i sin 4? What's the general rule for these kinds of numbers? Homework Equations e^{i\theta} = cos \theta...

I may be asking a stupid question, but what is the co-relation between the complex plane and the real plane? I know Euler's equation ei\pi+1=0 relates them, but graphically, how are they related?

[SOLVED] Urgent help needed with complex numbers Homework Statement a complex no. z is represented by the point T in an Argand diagram. z=\frac{1}{3+it} where t is a variable show that z+z*=6ZZ* and that as t varies,T lies on a circle, and state its centre Homework Equations...

Homework Statement Simplify (1+i\sqrt{2})^5-(1-i\sqrt{2})^5 Homework Equations z=a+bi z=r(cos\varphi+isin\varphi) tg\varphi=\frac{b}{a} r=\sqrt{a^2+b^2} The Attempt at a Solution...

Homework Statement Hello! :smile: a)Prove that (a+bi)^n and (a-bi)^n, n \in \mathbb{N} are conjugate complex numbers; b)Prove that quotient of any two numbers from the set of \sqrt[n]{1} is again number from the set of \sqrt[n]{1} c)Prove that reciproca value of any number from the...

Hi There, Can someone please tell me where I can find a table/ data that converts radians to surds. I don't know what to call it but, for instance to tan^-1(-1) = -Pi/4 and, cos(-pi/6) = root3/2 ? Thank you :)

4 Questions: (1 + i) / (1 - i) Ans: i (2 + 3i) / (5 - 6i) Ans: (-8+27i)/61 1/i - (3i)/(1-i) Ans: (3-5i)/2 i^123 - 4i^9 - 4^i Ans: -9i Could someone please explain the method (detailed) as to how these answers were obatined? I understand other questions in the same...

URGENT: Complex Numbers Problems: HELP NEEDED FOR MY FINAL EXAM!? Q1: Write the numbers in the form a+b: i) (2+3i)/(1+2i) - (8+i)/(6-i) ii) [(2+i)/(6i-(1-2i))]^2 Q2: Simplify: i) i^11 ii) i^203 Q3: Show that the points: 1, -1/2 + (i*squareroot(3))/2, -1/2 -...

Homework Statement Lets find the set of points z in the complex plane which satisfy the condition: a)|z-a|=r , r>0 where a is fixed point from the same plane, and r is positive real number. b)|z-a|=|z-b|, a \neq b Homework Equations The Attempt at a Solution I don't know...

Hi! I was just wondering if anyone would be able to help me with a question I received recently as complex numbers homework and didn't quite understand. There was an equation given in complex form ie. something along the lines of |z-2|=|zconjugate=2| (I cannot remember this exactly now...

hi, please help me

hi, let z=x+iy z^2=z.zpar=(x+iy)(x-iy)=x^2+y^2 or z^2=(x+iy)(x+iy)=(x^2-y^2)

Homework Statement http://imageshack.us" how are the solutions of the fourth roots pi/2? how do you get pi/2, you know the thing after "cos" and "isin" ?

[SOLVED] integral with complex numbers Hi, I feel really silly for asking this question... but can anyone give me any advice on how to evaluate the following intergral: \int\int\intr.e^{iqrcos(\theta)}sin(\theta)dr.d(\theta)}.d(\phi)} basically an integral spanning whole of space (I've...

Homework Statement B= 4-j2. Find \sqrt{B} in rectangular and polar notation. Homework Equations n/a The Attempt at a Solution i can figure out that in rectangular form by using the calculator and converting those back into polar form but how can i do this without calculator?

Hello all, My first post here and sorry it is not very scholarly. lol I am currently taking Algebra 2 and am completely lost as how to find the answers to simple equations and expressions such as the ones below. Can anybody help me out or if you own a TI-89 Calc and know how to perform...