Complex numbers Definition and 724 Threads

Hello, I'm having trouble with this problem: \left| \frac{(\pi + i)^{100}}{(\pi - i)^{100}} \right| = \ \ ? My first thought was, "put it in polar form and simpify," but that is not helping. For the numerator pi + i : r = \sqrt{\pi^2 + 1} \theta = \arctan{ \frac{1}{\pi} }...

My friend and I have to do an experiment for Physics. We chose complex numbers and we wanted to experiment with AC power. Our teacher said the experiment should consist of measurements so that we would have actual results and get a conclusion out of that or something like that. Does anyone...

Hi! I'd a look at complex numbers and can't understand how they can be applied to "the real world". Can anyone give me some concrete examples, please. Or a site that does. Danne

I've been attending at high school and I have some ideas about complex numbers. I shared my thoughts with my math teacher. He decided to search. I want to make sure if none have thought them so I need some information about complex numbers. Could you offer me some written sources and the...

Could someone please show me how: z_1\bar{z_2} + \bar{z_1}z_2 = 2\:Re(z_1\bar{z_2}) where \bar{z} is the conjugate of z.

The time independent schrodinger equation doesn't involve complex numbers. The time-dependent equation does involve complex numbers. When a complex number appears in an equation or expression can we assume that there is some underlying relation to time? So if I had a probability such as 1/4 +...

Can anyone help me with this: Let w be a complex number with the property w \leq 2. Prove that w can be written as a sum of to complex numbers on the unit circle. That is; prove that w can be written as w = z_1 + z_2, where |z_1| = 1 and |z_2| = 1. I really can't come up with a...

are complex numbers part of the "real" world The square root of -1 is used a lot in physics. But how does it relate to what,I suspect,most people would regard as the real world i.e real numbers (for example we speak of real probabilities and not imaginary probabilities - real probabilities...

i^57 is simplified to i ?

Z^6 + 64 = 0 there are suppose to be 6 solutions :confused: need help on how to find the roots

Let Z1 = 3-i Z2=7+2i express (1/Z1)-(1/Z2) in form a+bi SOMEONE pleasezzzzzz HELP ME! I don't have a clue as to how to do this :cry: What do I do? Where do I start? :cry:

If someone could give me some notes explaining about them that i could follow so i can do my homework and stuff it would be appreciated! I don't understand them at the moment b/c i don't understand the teacher, which is definately my problem. So it would be nice if i could get an explanation...

How does... e^{\frac{1}{2} i n x} = \sin{ \frac{1}{2} n x} ...where n is any positive integer and x is any angle. I know about de Moivre's Theorem, but that can't be deduced from there. There is also brackets around it, with some sort of greek letter on the outside. Looks like a...

It says that: x^2=the conjugate squared, which is: (a+bi)^2=(a-bi)^2 How can I show this? This isn't homework or anything, but I don't get where they got this from. I'm reluctant to move on until this is solved or understood.

How do you evaluate this type of problem: (5+2i)=SQRT(x+iy)

How do you evaluate this expression algebraically. e^{\sqrt{i}}

1. Are the HAMILTON‘ian unit vectors i, j, k still valid beside the imaginary unit i(Sqrt(-1))? Can we expand quaternions using complex numbers? 2. Is the quaternion a+bi+0j+0k equal to the complex number a+bi ?

Using converse of alternate segment theorem (i think it is) i.e. this: "If the line joining two points A and B subtends equal magnitude angles at two other points on the same side of it, then the four points lie on a circle" establish the cartesian equation, range and domain of the locus...

Hi...i was wondering if someone could confirm if what i have below is correct...thanks...sorry i can't present a diagram... z(1) = x + iy and z(2) = x(2) + iy(2) are represented by the vectors OP and OQ on an argand diagram...(O is the origin)...imagine the argand diagram...the upper left...

Hi... my notes show the solutions to four complex numbers showing how arg(z) is obtained...they also show an argand diagram showing theta...there's a couple of things i don't understand so i was hoping that someone could shed some light...thank you... (i) z = 1 + i (ii) z = -1 + i...

u noe how x^5=1 has 5 roots which some of them are not real in complex field. and so is x^2=-64 with roots = -8i or 8i and i notice that the sum of roots = 0 (msut inculde non real --> complex number) is this becasue of the rule of polynomial --> -b/a =...

My doubt is what are complex numbers used for. Sure I can use them to solve eqns where there are no real solutions. But how does that help. What is the real life application of complex numbers.

z1 = x + iy z2 = x - iy (Complex conjugate) Find: Im (1/z1) This is what I have tried to do: (1) z1*z2 = x^2 + y^2 (2) z2 / (x^2 + y^2) = 1 / z1 The answer is: -y / (x^2 + y^2) = I am (1 / z1) So my question is: Can I change z2 to I am (z2) and z1 to I am (z1) in...

I'm trying to find the: 4 4th roots of [itex] {\sqrt{3}} [/tex] + i . So I made a Cartesian plane and graphed radical 3 and 1.. but these numbers can be in 2 quadrants, 1st and 3rd. r=2 ==> 2([itex] {\sqrt{3}} [/tex] + i) ===> 2(cos 30+isin 30)...