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AOA... There are three question

1. I want to convert exp(Iota*theta) into ternometric function i.e., 

exp(Iota*theta) = cos(theta)+Iota*sin(theta)

Is there any comand pl help...

2. Also i want to rationalize the complex number...

3. I want to seprate real and imaginary parts of a comaplex numbers

 

 

(1/2)*(-x-y+sqrt(-3*x^2-6*x*y-3*y^2))/(x+y)

 

the complex value is always a constant whatever x and y 

i suspected that this is a wrong function

I am getting a complex solution for a physical quantity, how can I plot it. Should I plot the real part or modulus?

solution is,

C1*sqrt(4*tau^2*M^2*lambda^2+Q^2)*LegendreP((1/2*I)*sqrt(7)-1/2, I*sqrt(7), (2*I)*lambda*M*tau/Q)+C2*sqrt(4*tau^2*M^2*lambda^2+Q^2)*LegendreQ((1/2*I)*sqrt(7)-1/2, I*sqrt(7), (2*I)*lambda*M*tau/Q)

 

where C1 and C2 are integration constants.

1.which rules or theorems can guide to generate relations for words in group theory?

2.Is topological method such as complexes the direction to answer Question 1?

restart:

lambda1:=(1/(K+2))*(S+sqrt(2*alpha*(K+2)+S^2));

lambda2:=(1/(K+2))*(S-sqrt(2*alpha*(K+2)+S^2));

where K>=0, S (-15, 15) and alpha (-15, 15). While plotting for small values of S and alpha, I get complex roots.

  • How we can avoid the complex roots?
  • Is it possible to impose a condition in plotting? 

    solve(lambda1=lambda2,S);

    solve(lambda1=lambda2,alpha);

    solve(lambda1=lambda2,K);

  • How to single out the range of S and alpha for which we have complex roots?

Thanks

 

so we have to Write a function that diagonalises a complex (2x2) matrix if possible,  

we need the argument to be a (2x2) matrix say A.   and we need the return value to be a list [a1 ;a2 ;b1;b2] of two complex numbers followed by two 2-vectors such that {b1,b2} is a basis for C^2 and so that  

Ab1 =a1b1 , Ab2=a2b2  if these exist. if not then the function should return an empty list []

also, the thing is that we're not allowed to load any maple packages, we have to do it by hand :'(

thanks <3

 

-.733448502640020+0.*I

i am investigating above numeric

when ln(-.733448502640020+0.*I);

 

-.3099978916+3.141592654*I

it has Pi imaginary part

then 

i try 

complex(1, exp(Pi)^3);

it return Complex(...) but not 1 + i*exp(Pi)^3

 

3 means 3 times come from recursively  using pattern ln(Re(ln(x) - 3.141592654*I))

3.141592654 in imaginary part appear 3 times

i use Round(Im(x), 8) during above operation

 

 actually i want to extract Pi imaginary part from -.733448502640020+0.*I

 

however, after minus exp(Pi) from it first time,

it is near the original number  -.733448502640020

is this elimination of imaginary part is just a illusion from log function?

I am using maple (version 12) for the first time.  I want equations of x and y ( in terms of a) from these two given equations. The equations I got are very complex, how to simplify these equations?

 

Equation#1 is:


Equation#2 is:

From Equation#1, i find "y"

  

Now i put y in Equation#2

and from that euation, i can get x



but these equations are very complex..

I simply want to find the equations of x and y..
How to simplify it?

 

 

 

Here is the question:Prior to this question I was given f(z)=z^2+1, N(z)=(z^2-1)/(2z), T(z)=z-I/z+I such that T(N^k (z))=(T(z))^2^k. And L is a set of number on the real axis. Now the question is that given we have two regions of the complext plane as follow:

R+ = {z : Nk{z) -> i as k -> ∞}; R- = {z : Nk(z) -> -i as k -> ∞}.

Draw a diagram to illustrate these regions, the line L and the roots i and -i. We call R+ the basin of attractionfor the root +i, and similarly R-is the basin of attraction for the root -i.

 Show that if z is on the set L (the common boundary of the two regions R+ and R_, then Nk(z) stays on L for all values of k. (This is easy once you identify what L is.) So in this case iteration does not produce a root at all.

So basically my problem is that the fact I'm not very familar with the commands to draw such diagram, and I don't know much about Newton's method to compute complex roots. It would be appreciated if anyone can help me how to get start with the question. Thanks.

 

Hi,

New to maple and I have 2 questions that I'm stuck on.

 

1) Find the principal arguments of the 5 roots of the polynomial

and enter a decimal approximation to the largest principal argument in the box below.

ans: 2.589502038

 

2) Find the moduli of the 5 roots of the polynomial

and enter a decimal approximation to the largest modulus in the box below

ans: 2.34880159160143

 

I dont really know what to write in maple to get the answer. So, if someone could help me out that would be really great. cheers

 

 

 

 

Let z be a complex number and p your conjugate. how to solve the equation

(2z-3)(-3p+4)-(2p-3)(-3z+4)=0   with maple?

I have a numerical procedure that reads data from a file and builds a composition of maps from the half-plane to the slit half-plane.  Maple does not deal with this very well symbolically.  I want to use the complex values from this function as a vector field and plot some integral curves.  The 'mystery' function below is a stand-in for the real thing*

I can get DEplot to at least show the vector field, but it fails mysteriously on drawing any curves,...

with(Physics):

u := subs(x3=x3(t),subs(x2=x2(t),subs(x1=x1(t),u)));u := -Physics[`*`](Physics[`*`](Physics[`*`](3, Physics[`^`](conjugate(x2(t)), 2)), x2(t))+Physics[`^`](x1(t), 2)-x3(t), Physics[`^`](1+Physics[`*`](3, Physics[`^`](conjugate(x2(t)), 2)), -1));

u = subs(conjugate(x3(t))=x3(t),subs(conjugate(x2(t))=x2(t),subs(conjugate(x1(t))=x1(t),u)));

would like to remove all conjugate back to normal variable

I need to solve the following equation:

>restart;
>z := a+b*y*conjugate(y) = 0;

where y*conjugate(y) is unknown. How to solve it or how to eliminate y*conjugate(y) from the equation?

Thank you.

Please help me with transformation of the following expression:

> z:=abs(a)^2*b+abs(a)^2*c*conjugate(a);

where I want to derive

a*(conjugate(a)*b+conjugate(a)^2*c)

I try the following:

> z:=collect(z,a);

However it does't transformate z in any way.

 

In other words if I have
>z:=a*conjugate(a);

>z:=simplify(z);

I derive z=|a|^2. How to decompose z back into a*conjugate(a)?

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