Complex numbers Definition and 724 Threads

How do I express the following in the form a+ib? (\sqrt{-4} - 1) (\sqrt{-9}) My attempt: (2i - 1)(3i) 6i-3i = 3i

I need some help with converting this to cartesian form. z=-1+1i On a graph the relation is (-1,1) Then I use the pythagorean theorem to find the hypotenuse which works out to be the square root of 2. How do I then find what the angle of the triangle is using the unit circle?

[SOLVED] Complex numbers as an abelian group Homework Statement Multiplication of complex numbers defines a binary operation on C^x:=C\{0} (complex numbers not including zero). Show that C^x together with this binary operation is an abelian group. (without further discussion you may use the...

Hey, When solving polynomials over c that have complex coefficients such as: z^3+(5i-4)z^2+(3-20i)z+15i what is the easiest way to find your first factor? My textbook says to use the factor theorem, if you agree is there a quicker way to find a factor than by trialing the constants factors...

[SOLVED] Complex numbers linear algebra Homework Statement Let w, z be complex numbers. Solve the linear equation wx=z; in other words find all x (of the set of complex numbers) such that wx=z. (hint: You need to distinguish 3 cases) Homework Equations The Attempt at a Solution...

Homework Statement Find the roots of the equation z^3=-(4\sqrt{3})+4i giving your answers in the form re^{i\theta}, where r>0 and 0\leq \theta<2\pi Denoting these roots by z_1,z_2,z_3, show that, for every positive integer k. z_1^{3k}+z_2^{3k}+z_3^{3k}=3(2^{3k}e^{\frac{5}{6}k\pi i})...

can anyone give me a detailed explanation on how to derive equation for a straight line, which is made up of points, each point representing a complex number..// pls help

Homework Statement Evaluate each of the following complex numbers and express the result in rectangular form: a) 4\,e^{j\frac{\pi}{3}} b) \sqrt{3}\,e^{j\frac{3\pi}{4}} c) 6\,e^{-j\frac{\pi}{2}} d) j^3 e) j^{-4} f) \left(1\,-\,j\right)^2 g) \left(1\,-\,j\right)^{\frac{1}{2}} Homework...

how do I show that: |y + x|^2 = |y|^2 + |x|^2 + 2|yx|cos(a1-a2) where y = |y|exp(ia1) and where x = |x|exp(ia2) and how do I show that |exp(z)| = exp(Re(z)) where Re is the real part of an imaginary number z. thanks is advance

find all complex numbers satisfying z^3=-8 i have no idea how to solve this can someone help please? thank u

We used complex variables to describe the wave function. People do that in acoustics and optics too, strictly for convenience, because the real and imaginary parts are rudundant. The wave function of quantum mechanics is "necessarily" complex, it's not just for convenience that we use complex...

[SOLVED] Complex Numbers A very happy new year to all at PF. Homework Statement Kreyszig, P.665 section 12.3, A function f(z) is said to have the limit l as z approaches a point z_0 if f is defined in the neighborhood of z_0 (except perhaps at z_0 itself) and if the values of f are "close"...

[SOLVED] Complex Numbers: Eigenvalues and Roots Below are some problems I am having trouble with, the computer is telling me my answers are wrong. It may be the way I am inputting the numbers but as my final is in a week and a half I would like to be sure. Thanks,

\sqrt{z}=\sqrt{r}(\cos \frac{\theta}{2} + \pi \ + \ \iota \sin \frac{\theta}{2} +\pi)\\ ...(i) Obtain from equation (i) this equation \sqrt{z} \ = \ +/- [\sqrt{\frac{1}{2} (\abs{z} + x)} \ + \ \mbox{ sign y} \ \iota \sqrt{\frac{1}{2} ( \abs{z}+x)}]\\ . Where sign y =1 it y greater than or...

I should just give math up, I don't understand this at all. It seems like for a) the function could be squared, and other than that it doesn't make any sense. Let V = {p element of R[x] | deg(p) <=3} be the vector space of all polynomials of degree 3 or less. a) Explain why the...

Homework Statement The set of complex numbers C is a vector space over R. Note that {1, i} is the basis for C as a real vector space. Define: T(z) = (3+4i)z What is the matrix for T in the basis {1,i} Homework Equations Dimension of the matrix (n,m) = n x m The Attempt at a...

Okay. I'm just looking for someone to check my answer to the following question! I'm not sure this is the correct forum for such a question, if not, feel free to have it moved :) QUESTION: An a.c. supply of amplitude 20V and a frequency of 5 kHz is connected across a Resistor R = 4.7...

complex numbers problem...need help Hi all Could anyone out there please help me with the solution to this problem. Express 2.91e to the power of 1+j2 in Cartesian form (x+jy) Sorry writing it out, but I don't know how to set it out on the computer. I have tried solving the 1+j2...

Hello Me and my friend were discussing about an irrelevant subject when he said that 1+1 is not always equals to 2 mathematically due to complex number variations. Can anyone highlight the influence of complex numbers on this equation?

Homework Statement find the three roots of z^{3} = 1, giving non real roots in the form of e^{i\theta}, where -\pi<\theta\leq\pi Homework Equations z = re^{i\theta} The Attempt at a Solution i kno that one of the roots is 1, an the other two form a conjugate pair. i can't find them.

Homework Statement U-i*V=ln((z-1)/(z+1)) - solve for U and V, where U is the real part and V is the imaginary part, of this equation Homework Equations z=x+i*y, where x and y are the real and imaginary parts respectively The Attempt at a Solution I've attempted raising it to the...

I can easily solve systems of equations with no complex numbers, could somebody give a short overview of the easiest way to do this by hand. thanks

1) A mathemetician is willing to sell you something valued at $i^i. Would you pay him 20 cents for it? 2) Let z=(z1/z2) where z1 = a+ib and z2 = c+id. Show the angle of z is the difference between angle z1 and z2. 3) Show that multiplying any vector by e^ix doesn't alter its length...

[SOLVED] Complex Numbers Homework Statement I was given an equation with complex numbers, and told to convert to polar coordinates. I was able to find r relatively easily, but finding the angle is giving me trouble- I am having difficulties in breaking the equation down into imaginary and...

Express this in terms of j 6j-5j2√-63 I have no idea how to do the ones with square roots, my teacher is lost. Completely and I am stuck on this 1 number for like 2 hrs trying to figure it out. The answer is sopose to be -28j please help me out **Note that j2= -1 NOTE ALSO THAT...

hi, I am trying to solve this equation and i would like some help. i've done some of it already and i don't know how to go on from here. z=-\frac{(4-4i)(\sqrt{6}-i\sqrt{2})}{i}\\ =-\frac{(4-4i)(\sqrt{6}-i\sqrt{2})-i}{i(-i)}=(4i+4)(\sqrt{6}-i\sqrt{2})\\ \hspace{6}...

(a)Find all t \epsilon C such that t^{2} + 3t + (3-i) = 0. Express your solution(s) in teh form x+iy where x,y \epsilon R. (b) Prove that | 1+iz | = | 1-iz | if and only if z is real. Okay so I tried to use the quadratic formula to find the roots to find the solutions, but I am stuck...

Complex numbers - polar form - does this work (indices) ? hey i haven't studied in class complex numbers yet, but i know some of the basis , and i was wondering if something i saw in complex numbers was true : polar form : let 'a' be the angle and x the length (dont know how to call it...

Consider the complex number z=e_{i\theta} = cos\theta+isin\theta. By evaluating z^{2} two different ways, prove the trig identities cos2\theta = cos^{2}\theta - sin^{2}\theta and sin2\theta = 2sin\thetacos\theta. A question about the approach to this question: How do you guys approach the task...

I was playing around with complex exponentials and came to this result: $\begin{eqnarray*} e^{\frac{2\pi i}{5}}&=&e^\left(\frac{2}{5}\right)\left(\pi i\right)\\ &=&\left(e^{\pi i}\right)^{\frac{2}{5}}\\ &=&\left(-1\right)^{\frac{2}{5}}\\ &=&1\end{eqnarray*}$ But obviously e^{\frac{2\pi...

I read in an article that the theory of Electromagnetism makes use of Complex Numbers. How are the tools and tricks of Complex Numbers used in Electromagnetic theory. I just wanted to understand the basics of this connection of Complex Numbers and Electromagnetism and figure out if this...

Homework Statement A circuit is said to be in resonance if it's complex impedance Z (in terms of R, L, and C (being the resistance, inductance, and capacitance)) is real. We are to determine the resonance angular frequency \omega in terms of R, L, and C. Homework Equations The circuit is...

Hello everyone. i got one interesting homework. So... i need write about complex numbers. I already found many materials for that homework but... i stuck in one interesting point. I must write a pretty complicated task(teaser). i must think that task myself. Like simply task...z=a+bi---> 3+8i...

Homework Statement Given that z=(b+i)^2 where b is real and positive, find the exact value of b when arg z = 60 degrees. Homework Equations z=a+bi arg z=arg tan \frac {b}{a} The Attempt at a Solution so I expanded my z=(b+i)^{2} so its z=b^{2}-1+2bi On other terms (please note the b here...

Homework Statement I have an exam coming up on Monday, and I can't seem to solve this question. Please point me in the right direction. x=e^{i\alpha}, y=e^{i\beta} z=e^{i\gamma}. If x+y+z=xyz, prove that, cos(\beta -\gamma) + cos(\gamma -\alpha) + cos(\alpha -\beta) + 1=0 Homework...

need sites for solved problem pls... anyone know a website that has solved problems for complex numbers (multivariable calculus)? my finals is on Monday and there aren't enough sample problems in our book, some are very basic.. i really need help..

hey i know the basics about complex numbers like: 5*i^7 = 5*i^3 = 5 * -i = -5i = (- pi/2, 5) but now : how would i represent : -> 1 ^ i = ? = ( ? , ? ) or would it involve another mathematical dimention and be more of a (? , ? , ?) ? //////////////////// and now, how can i...

Homework Statement 1) If I know that z_1 = (2+i) and z_2 = (2-i) are solutions to a polynomial, how do I find it? (I have six to chose between, it's a multiple choice). Do I just insert and see of it equals zero? 2) When I know that z^2 has modulus 4 and argument pi/2, how do I find...

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 Express cos^{-1}(x+iy) in the form A+iB). The Attempt at a Solution x+iy=cos(a+ib) x-iy=cos(a-ib) 2x=2cos(a)cosh(b) x=cosa coshb Similarly, y=-sina sinhb Using these values, I got x^2+y^2=cos^2a +sinh^2b, but I don't know where to go from here. Alternatively...

I just came across the eq. z^2 - 2z + 1 - 2i where z is a complex number. How do I solve this sort of eq.? I tried to solve it as a normal 2nd degree eq., setting a=2, b=-2 and c=(1-2i), with z as the variable. This finally gave me the solutions z(1) = -1 + sqrt(2i) and...

Out of curiosity, what happens when you try to perform a trig function on a complex number? So, say, sin(4i+3)? Is this undefined since angles are only capable of being real numbers, or is there an agreed behavior for complex numbers? DaveE

IS there a formula for: z=(Cosx +iSinx)^4 (Cosy + iSiny)^2 ??

I was never good at trigonometric identities. Let z= cos x + i sin x Express 2/(1 + z) in the form 1 - i tan kx I need help. A pointer to where to start would be great.

Hello I got some funny idears don't know if they are true, but I will share them with you. Homework Statement I would like to prove these formula (1)sin(z_1 + z_2) = sin(z_1) \cdot cos(z_2) + sin(z_2) \cdot cos(z_1) (2)cos(z_1 + z_2) = sin(z_1) \cdot sin(z_2) - cos(z_2) \cdot...

Homework Statement Express -i in polar form, using the principal value of the argument. Homework Equations modulus = \sqrt{a^2 + b^2} \theta = arg(0 - i) The Attempt at a Solution Well, the complex number is 0 -i. a = 0, b = -1 so: r = \sqrt{0^2 + (-1)^2} which comes out to...

Hello guys; I'm after a bit of help here, I may have missed something completely obvious, but I can't seem to figure out the working of: [FONT="Arial"]1 + i = √2(cos π/4+ i sin π/4) ie; How does 1 + i equal √2(cos π/4+ i sin π/4)?? any help would be appreciated; Thanks...

1. Complex analysis is the study of number z= x+iy where i^2=-1. can you find a way to represent complex numbers as 2x2 matrices i honestly have no clue where to start with this one. we are one week through my linear algebra course. the only possible thing i can thing of is det (x -yi...

Here is another problem that I'm not sure how to approach A Circuit consisting of a 500 Ohm Resistor in series with a 1.2 micro F capacitor is connected to a supply at a frequency of 400Hz. Use complex numbers to determine the values of resistance R and capacitance C, that when connected in...

Hi, here is the problem.. The potential difference across a circuit is represented by 40 + j25 volts, and the circuit consists of a coil with an inductance of 0.06H in series with a resistance of 20 Ohms. If the frequency is 80Hz find the complex number in rectangular form that represents the...