how to write fraction function in complex plane by using matlab
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Hi
I worked in ploting function defined in complex plane by using matlab I know we can write the polynomial in matlab by using its coefficients
for example f(z)= (2-8i)Z^3+(2+3i)Z^2 + (1+5i)Z+ (3-4i) this equation can be written in matlab as p=[(2-8i) (2+3i) (1+5i) (3-4i) ],. But when we find this equation f(z)= (2-8i)/Z^3+(2+3i)/Z^2 + (1+5i)/Z+ (3-4i) how can I write this equation in matlab? I mean here the complex variables in the Denominator
Thanks
1 个评论
Benjamin Thompson
2022-2-8
MATLAB supports complex numbers. See documentation on the topic "complex". Are you trying to write the equation symbolically using the Symbolic Toolbox, or numerically to calculate answers at specific values of Z or to plot over a range of the complex plane?
采纳的回答
MATLAB has a simple form to allow you to store only the coefficients of a polynomial. You aready know that. But there is no simple form to allow you to store some arbitrary function. In this case, you wish to store the coefficients of a function that uses inverse powers of a variable Z. Luckily, you can cheat, just a bit. That is, if you have the coefficients as a vector as you do here,
(2-8i)/Z^3+(2+3i)/Z^2 + (1+5i)/Z+ (3-4i)
So you have just the vector:
p = [(2-8i) (2+3i) (1+5i) (3-4i)];
Then you can evaluate it using polyval as:
z = 1:3;
polyval(p,1./z)
That is, we just think of this as a simple polynomial in powers of 1/z, so compute the inverse of z, THEN use polyval on those values.
5 个评论
Aisha Mohamed
2022-2-9
Benjamin Thompson
2022-2-10
What are you trying to do with this complex valued function? Do you want a plot over a range of the complex plane, or trying to define the function symbolically to use it in some other way?
Aisha Mohamed
2022-2-13
I did not ignore two things. I answered the question you asked. You did NOT ask how to find the zeros of a function. You asked how to write what is effectively a polynomial in 1/Z.
My choice of 1:3 is irrelevant, I picked it as an example.
You then say that polyval may not be appropriate. Why not? It evaluates the polynomial that you give it. For example, you gave these coefficients.
format long g
p = [(2-8i) (2+3i) (1+5i) (3-4i)];
z = 1 + 3i;
polyval(p,1./z)
Is that the correct value? Test it.
sum(p.*z.^(-3:1:0))
Note that the above line of code applies ONLY for scalar values of z. However it clearly agrees with polyval.
As far as zeroes goes, please show me where in your question where you EXPLICITLY said even a single word about the zeros of this function? Here is the statement of your question, just in case you forgot:
"I worked in ploting function defined in complex plane by using matlab I know we can write the polynomial in matlab by using its coefficients
for example f(z)= (2-8i)Z^3+(2+3i)Z^2 + (1+5i)Z+ (3-4i) this equation can be written in matlab as p=[(2-8i) (2+3i) (1+5i) (3-4i) ],. But when we find this equation f(z)= (2-8i)/Z^3+(2+3i)/Z^2 + (1+5i)/Z+ (3-4i) how can I write this equation in matlab? I mean here the complex variables in the Denominator:"
That was your exact statement. Yes, you finally added the word zeros in a final comment. Sorry for expressing irritation, but should I be able to read your mind? SIGH. Maybe you were thinking about zeros. But don't tell me that I did not answer the question you asked.
Ok. You want to find the zeros of this function? Still trivial.
proots = 1./roots(p)
Now evaluate the function at those points. I will use polyval.
polyval(p,1./proots)
So zero, to within floating point trash. proots contains the zeros of the indicated polynomial in powers of 1/z.
Aisha Mohamed
2022-3-14
更多回答（1 个）
Sphiwe
2023-10-15
0 个投票
num = [1]
den= conv([1 3 5], [1 3], [1 5])
g = tf (num,den)
[z,p,k] = tf2zp(num,den)
pzmap(g)
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