nth root of complex numbers. ask for input of complex number in the form a+bi, and input the n for the nth root of the complex number without using the nthroot function in matlab

To calculate the nth root of a complex number without using the nthroot function in MATLAB, you can use the following steps:

1. Prompt the user to enter the complex number in the form a+bi and store it in variables a and b.
2. Prompt the user to enter the value of n for the nth root and store it in a variable n.
3. Calculate the magnitude (r) and argument (theta) of the complex number using the formulas:
   • Magnitude: r = sqrt(a^2 + b^2)
   • Argument: theta = atan2(b, a)
4. Calculate the nth root of the magnitude using the formula:
   • Nth Root of Magnitude: r_n = r^(1/n)
5. Calculate the nth root of the argument using the formula:
   • Nth Root of Argument: theta_n = theta/n
6. Calculate the real (x) and imaginary (y) parts of the nth root using the formulas:
   • Real Part: x = r_n * cos(theta_n)
   • Imaginary Part: y = r_n * sin(theta_n)
7. Print the resulting nth root of the complex number as x+yi.

Here is the implementation in MATLAB:

main.m
% Step 1: Prompt user for complex number
prompt = 'Enter the complex number (a+bi): ';
complex = input(prompt, 's');
[a, b] = sscanf(complex, '%f+%fi');

% Step 2: Prompt user for nth root
prompt = 'Enter the value of n for the nth root: ';
n = input(prompt);

% Step 3: Calculate magnitude and argument
r = sqrt(a^2 + b^2);
theta = atan2(b, a);

% Step 4: Calculate nth root of magnitude
r_n = r^(1/n);

% Step 5: Calculate nth root of argument
theta_n = theta/n;

% Step 6: Calculate real and imaginary parts of nth root
x = r_n * cos(theta_n);
y = r_n * sin(theta_n);

% Step 7: Print the resulting nth root
fprintf('The nth root of %s is %.4f+%.4fi\n', complex, x, y);
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It's important to note that due to the nature of complex numbers, there can be multiple solutions for the nth root. The above code calculates only one of the possible roots.