I need help with complex numbers?
You need to separate the real components from the imaginary ones. 3x = 12 + x 2x = 12 x = 6 and -4i = 2yi 2y = -4 y = -2 ~Zara Sahana
Help needed for Complex number!?
Please help me.. Suppose that f is holomorphic on the region G and f(G) is a subset of the unit circle. Show that f is constant. (Hint: Consider the function (1+f(z)/1-f(z))).
Need help with maths- complex number?
1) Two complex numbers, z and w, satisfy the inequalities I z-3-2i I≤2 and Iw-7-5i I≤1. By drawing an Argand diagram find the least value of I z-w I 2) a) The complex number z satisfies the equation (z + 2i/k)(1/z -2i/k) =1, where k is a positive real number. Obtain a quadratic equation for z, and show that its solution can be expressed in the form ikz=a±square root(bk²+ck+d) for suitable real numbers a, b, c, d. show that z is purely imaginary when k≤1. b) A second complex number α is defined in terms of z by α=1+2i/kz. What can be said about α when k≤1? Show that IαI=1 when k≥1. c) A third complex number β is defined by 1/β=1-i/k. by finding the real and imaginary parts of β-ki/2, show that β lies on a circle with the centre ki/2 and radius k/2.
Complex Numbers Help?
The question asks you to find the cube roots and sketch them in the complex plane. The problem is to find all the cube roots of z, where z = (sqrt3)/2 + 1/2i. I found the roots to be the following: cos(pi/18) + isin(pi/18) cos(13pi/18) + isin(13pi/18) cos(25pi/18) + isin(15pi/18) Now i need to sketch them in the complex plane...how do i do this and what does it look like??? Thank you in advance!
Need a help in // COMPLEX NUMBER // problem ....?
ω³=1 and 1+ω+ω²=0 f(a,b,c) = (a+bω+cω²)³ + (a+bω²+cω)³ is homogeneous and symmetric in a,b,c (see **) ∴ f can be expressed as a homogeneous polynomial in the elementary symmetric functions for 3 variables ie f(a,b,c) = α(a+b+c)³ + β(a+b+c)(ab+bc+ca) + γabc for unique α,β,γ In fact, f(a,b,c) = 2(a+b+c)³ − 9(a+b+c)(ab+bc+ca) + 27abc (see ***) If given hypothesis holds then (a+b+c) (2(a+b+c)²−9(ab+bc+ca)) = 0 So either a+b+c=0 or 2(a²+b²+c²)=5(ab+bc+ca) The second possibility is viable. I tried it with b=c=1, a=(5+3√3)/2 which has a+b+c≠0 http://www.wolframalpha.com/input/?i=Fin... ** Interchanging b & c clearly leaves it unchanged. If you interchange a & b and write (b+aω+cω²)³ + (b+aω²+cω)³ = ω⁶(b+aω+cω²)³ + ω³(b+aω²+cω)³ =(bω²+a+cω)³ + (bω+a +cω²)³, Then it is also unchanged. Similar for interchanging a & c. So f is symmetric in a,b,c. *** (a+bω+cω²)³ + (a+bω +cω²)³ ≡ α(a+b+c)³ + β(a+b+c)(ab+bc+ca) + γabc b=c=0 ⟹ a³+a³ =αa³ ⟹ α=2 a=b=c ⟹ 0 + 0 = 27αa³+27βa³+γa³ ⟹ 27α+9β+γ = 0 Equate coefficients of abc ⟹ 6+6 = 6α+3β+γ Solve for α=2, β=−9, γ=27
Why do we need complex numbers?
Complex numbers do not have a real physical meaning. That's why they are called imaginary numbers. But they are very useful because they make a lot of math consistent and easy to handle.I think the most important applications of complex numbers would be the following (no official source for this information, only what I feel):Signal processing: Most of electrical engineering relies heavily on complex numbers. So, all electrical appliances are based on principles that are very well formulated in terms of complex numbers.Eigenvalues : Eigenvalues occur naturally at a lot of places. Most systems will not have all real eigenvalues - so to deal with eigenvalues, you need to work with complex numbers.Fast Fourier Transform : The fastest known algorithm for multiplying numbers uses complex numbers at its center. Although you can achieve the same using algebraic structures like rings, but the whole idea was developed using complex numbers.
Complex Numbers help please?
Hello, I need a bit of help with complex numbers. :( Can someone show me how to calculate the cartesian (rectangular?) and polar forms of this example: [(2+5i * 1-3i) / (2+5i + 1-3i)] + 4-i Then the extra part is to convert the final answer to exponential form? What is that? Thanks for any help :]
What can I use complex numbers for?
Few problems are expressed naturally in terms of complex numbers. (For an exception see the last paragraph.) However, many problems are simplified by using complex numbers. The key to many of these is Euler’s formula [math]e^{ix} = \cos x + i \sin x[/math]. This can convert complicated formulae involving sines and cosines into exponentials. This helps in solving linear differential equations that arise from vibrations and alternating currents. Therefore complex numbers are used extensively in electronics.Complex numbers do seem to be necessary as a model for the real world in quantum mechanics, where the wave function is a complex function from which one can derive the probability that a particle will be found in a specific state.
Complex numbers problem need help Precalculus?
Here is part of it. z1 = -3 + sqrt(3) i The point on the complex plane is at exactly the same location as (-3, sqrt(3)) on the x-y plane. So you have a 30-60 degree right triangle, in QII, reference angle 30 degrees, and you can read off the polar form as: r ( cos t + i sin t) where t = 5pi/6 and r = 2sqrt(3) That is the polar form of z1, which I now see they didn't ask for. Oh well :(. The modulus of x+iy is sqrt(x^2+y^2) so the modulus of z1 = -1 - i is just sqrt(1 + 1) = sqrt(2). The polar form of z1 is r ( cos t + i sin t), with r=sqrt(2) and t=5pi/4. The product of two complex numbers in polar form is obtained by multiplying the moduli and adding the arguments, so the polar form of z1z2 is: (2sqrt(3))(sqrt(2)(cost + i sint) where t= 5pì/6 + 5pi/4 I'll leave "Big D" to you.
What is the need for complex numbers? I don’t think √-1 makes any sense.
O, reason not the need! The merest beggarIs in the smallest thing superfluous…I won’t try to explain why they are “needed”. Feel free, like the cowboy looking over Nieman Marcus, to say “I never knew there were so many things a man could do without”. However, I will question your notion about [math]\sqrt{-1}[/math] not making any sense.It’s impossible to be sure, you being so abrupt and all, but I’ll try to guess what your problem is.Your problem, I suspect, is that confronted by the idea of a number whose square is -1 you try to work out which number you already know will fit the bill. You can’t think of one - in fact, you’re quite sure there isn’t one - so, bingo, there ain’t no such number. That’s not how it works. That’s completely not how it works. [math]i[/math] was invented (I am telescoping a rather more complicated history here) to be a NEW number. It was invented specifically do do something that existing numbers couldn’t; it was invented to be a number whose square is -1. There’s no point in arguing about “whether it can do this”. You can ask whether the resulting algebra is a consistent extension of the algebra you already know of real numbers. The answer is “almost completely”; the notion of order is lost, but everything else “just works”. If you take mathematics far enough, you will be expectd to be able to show this yourself. [math]i^2 = -1[/math] because[math]i[/math] was invented to make this true.That leaves “but then it’s not a number!”. What makes something a “number” or not? Surely you aren’t going to say “if I haven’t seen it before, it’s not a number”! How about 354,261? Have you seen that before? Presumably there was a time when you knew hardly any “numbers”. Maybe you did stamp your little chubby feet on the floor and insist that there couldn’t be any “numbers” you didn’t know. I imagine you got over this in time. So also with [math]i[/math] and its friends-and-relations. You just get used to them. If you don’t want to call them “numbers”, that’s up to you; but if you want to be understood, and to understand what others are saying, you’ll allow them to be called “numbers”. Not because they “really are” numbers, or inspite of “really not being” numbers, but because things are called “numbers” because that’s what we call them.