Complex number Definition and 438 Threads

Homework Statement The question: a)Solve the equation z^{3}=4\sqrt{2}-4\sqrt{2}i.. b)Express the answer in polar form. The Attempt at a Solution Here's what i got: r=\sqrt{\left(4\sqrt{2}\right)^{2}+\left(-4\sqrt{2}\right)^{2}}=8 \tan^{-1}\left(\frac{-4\sqrt{2}}{4\sqrt{2}}\right)=-45^{o}...

hello could someone please help me out with proving the following: |z1|^2/|z2|^2 = |z1/z2|^2 ...with complex numbers sorry I am not familiar with the coding here yet so i can't write that properly

Homework Statement I need to find the solution to (2-11i)^{\frac{1}{3}} Homework Equations If (2-11i)^{\frac{1}{3}} were to equal (a + bi) for some real numbers a and b then 2 - 11i = a^3 +3a^2bi-3ab^2-b^3i The Attempt at a Solution From above a^3-3ab^2 = 2 and 3a^2b - b^3 =...

I am working through this algebra book and some of the problems. The chapter this comes out of is General Algebraic Systems and the section is Isomorphisms. I am new to proofs and maths higher than calculus I so I am not sure if I am following the text or not. There aren't any solutions and this...

How do we know when one complex number is greater than another? For instance, if a+bi > c+di, must a>c and b>d?

what is the magnitude and angle of this complex number? in terms of a and b? http://img364.imageshack.us/img364/4262/1af2.jpg come i need some help

Hey Everyone, I cannot seem to find an way in Matlab to convert a number which has a real and imaginary part in cartesian form into polar form and then express the polar representation on the output. Ex. Convert z=0.1602932442+0.8277219859*j Into 0.8431<79.04 deg (without using...

hi, is there any way to find the cube roots of a complex number WITHOUT converting it into the polar form? i am asking this because we can find the square root of a complex number without converting it. i was just wondering whether there is such a method for finding cube roots too. i was...

if z = 2 r cos x + r i sin x what is the value of lzl I worked for 3 hours but yet can only find lzl in terms of r and x, but the question says find the value, can anyone help solve? this is a special question to me because i always see polar forms with coefficient of the sin and...

Hello there, I've been given the task of find the real part for the following expression \sqrt{x+iy} And I'm a bit stuck. I figure that I'll just say that that equation is equal to some other imaginary number a+bi where 'a' is the real part and 'b' is the imaginary part, and try to solve for...

Calculate the real part, the imaginary part, and the absolute value of the following expression: i * [(1+2i)(5-3i)+3i/(1+i)]. So I did the math out this way: (1+2i)(5-3i)= 11+7i (11+7i)+3i/(1+i)= (4+21i)/(1+i) i * [(4+21i)/(1+i)] = (4i-21)/(1+i) Is this correct and what do you...

For this problem i am given two complex numbers Z_1 , Z_2 and then a third which is the sum of the first two complex numbers Z_3 . I am then asked to find the geometric interpetation of these numbers in \mathbb{R}^2 . I am fine when graphing them in the complex plane but unsure of what they...

Hi, how to solve this question? Find the square roots fo the complex number -40-42i. Hence (i) Find the square roots of the complex number 40+42i, (ii) solve the equation (z+1)^2 + 160 + 168i = 0 for all complex roots. I don't know how to start solving this question.

#2 Hi, Well can anyone tell me how to find the natural logarithm of a complex number p + iq. Also please tell me how to convert it into logarithm to the base 10. An external link to a webpage (where all the details are given) will be appreciated.

using eulers formula express cos5ø in terms of cosø. Hence show that =cos(pie/10) is a root of the equation 16x^4 - 20x^2 +5 =0 .. Thanks in advance .

how convert dis to cartesian form!? quation was here and then i will need to sketch on an argand diagram. help apreciated thnx

Hi I'm fairly new to complex numbers and was yesterday presented with the following assignment. Find w,z \in \mathbb{C} w + (1+i)z = -1 (1-i) - z = 1 Any hints on how to solve these equations? Sincerely Yours Mathboy20

I need to work out both cos and sine of (2-i). The answer needs to be in the form x+iy where both x and y are real. So far I have got: cos (x) = ( e^ix + e^-ix ) / 2 as a general formula which when I substitute in gives: 0.5e^(2i+1) + 0.5e^(-2i-1) How do I get this into the correct...

Hi everybody! Could somebody please assist me with an explanation as to why the following: arg (z+3-2i) = 135degrees : has its centre at -3,2 and that is the place where you begin the argument (ie go 135 degrees) Please note, just beginning complex numbers. Sorry if can't understand question...

This is a simple problem. Show that: (-1 + i)7 = -8(1 + i) where i = sqrt(-1) I'm able to prove this result by expanding the bracket: [(-1 + i)3]2(-1 + i) But please help me prove this using the polar form.

just having a problem with these 3 questions. z E C such that I am z=2 and z^2 is real find z well from my knowledge, it's will be x+2i, z^2 is (x^2 -4) + 4xi, since I am z= 2 then 4xi= 2? doesn't it, Umm don't really know what to do next 2nd questions z E C such that Re z= 2Im z, and...

How to proove that (x - a)(x - b)(x - c)... If a, b, c... are complex numbers, and none is conjugent to another the result will always be complex? Complex as is not real for those who like to complicate things...

Hello, I am trying to solve (z^4-2+i)(z^2+1-i)=0 With the quadratic formula: (z^2+1-i)=0 Does a=1, b=1 & c=-1? Thanks for your time. IM meant to (a) Give answers in polar form using the principal argument; (b) Give answers in cartesian form Cartesian is (x,y) is it not...

Someone solve this please! If z= CosA+iSinA, express 2/1+z in the form I-Tan(kA).

Hi, I'm looking at a question from my Pure 6 textbook (united kingdom), it's not actually for homework but I'd like to figure it out. First part of the question goes like this: If 2 cos θ = z + z^-1 prove that (if n is a positive integer) 2 cos n θ = z^n + z^-n. I can get a...

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Hello, I have this complex number that I need to convert to polar coord represntation: z = 1 + j; the answer is sqrt(2)e^-j45 (45 is degrees). The part I don't undestand is negative before j45, since a and b are positive, I assumed it's in the first quandrant of Im/Re plane, and if the...

Is there any law for finding the root of a complex number in catesian coordinates? without changing to polar, I've created 1, i just want to know is it worthy or not, so ... everybody who reads the message, please post the ROOT OF A COMPLEX NUMBER IN CARTESIAN COORDINATES LAW and let me...

Hi all, Im having a bit of trouble with a question. I have to convert: Ke^{j\delta} - Ke^{j\psi} Into the form re^{j\theta} This is the second part of the question, the first part was an addition instead of subtraction which i managed by using this formula: z_1 + z_2 =...

Can you help me with the following problems please. I have a course in telecommunications and i have to understand complex numbers first. I can't solve the following exercises: 1) Write in the form z=x+jy the complex number e^e^j ^=exp 2)how i can solve this equation |z+2|=|z-1| and...

Complex Number, again... :( This I'll give you the entire question and answer. 10. Solve: z^4-2z^2+4=0 That's all I got. Answer: +-1/2(\sqrt{6}+-\sqrt{2i}) (four combinations of signs). That is all. I tried factoring, but I can't come up with anything. I also tried...

The question is : The complex number z is given by z = 1 + cos (theta) + i*sin (theta) where -Pi < theta <= Pi Show that for all values of theta, the point representing z in a Argrand Diagram is located on a circle. Find the centre and radius of the circle. Note that i understand...

Hi All, I've been asked to determine the values of z that obey the equation e^z = 1 + sqrt(3)i I'm still not sure the concept of this question. Could someone point me in the right direction? Thanks

4 = \sqrt {4*4} = \sqrt {4*4*i^4} =\sqrt {i^2*4 *4*i^2} = i\sqrt{4}*i\sqrt{4} =2i*2i =-4 this is wrong but which setp =)

if a^k =1 and a \in \mathbb{C} k \in Z^+ and for some k A = \{a|a^k = 1\} does |A| = k ? edited: becasue the real numbers are a subset of the complex numbers

hope to get the idea on how to solve this question. the complex number z is given by z = 1 + cos (theta) + i sin (theta) where -pi < theta < or = +pi show that for all values of theta, the point representing z in a Argand diagram is located on a circle. find the centre and radius...

Heyas. I'm not too good at complex numbers so excuse me if these questions are a bit on the laughable side. Find all real values for r for which ri is a solution of the equation. z^4 - 2z^3 + 11z^2 - 18z + 18 = 0 hence, Determine all the solutions of the equations... I'm not really...

actually what is complex number... i know it's root of the -1 but how can we imagine the kind of number exist??