Question

MATLAB code help needed

(a):Write a single line of code that will take complex variables x and y and define a variable z as the phase of the product of x and y.

(b):Write a line of code that will form a variable z with magnitude r and phase phi.

(c):Write a line of code that will take complex variables x and y and define a variable z as the real part of x divided by the magnitude of y.

(d):Write a line of code that forms a vector z with real part given by the vector x and imaginary part given by the vector y. Assume x and y contain real numbers and are the same dimension.

Answer 1

(a) z = angle(x .* y);

(b) z = r * exp(1i * phi);

(c) z = real(x ./ abs(y));

(d) z = x + 1i * y;

Step-by-step explanation:

(a) In this code, the complex variables x and y are multiplied together using the ".*" operator, resulting in a complex product. The "angle" function is then used to find the phase of this product, and the result is stored in the variable "z".

(b) This code forms a complex variable "z" with magnitude "r" and phase "phi". The "exp" function is used to calculate the exponential of 1i times the phase, which gives a complex number with the specified magnitude and phase.

(c) This code takes the real part of the complex variable "x" and divides it by the magnitude of the complex variable "y". The "real" function is used to extract the real part of "x", and the "abs" function is used to find the magnitude of "y". The result of this division is stored in the variable "z".

(d) This code forms a complex vector "z" with real part given by the vector "x" and imaginary part given by the vector "y". The "1i" operator is used to create an imaginary number, and this is multiplied by the vector "y" to give the imaginary part of the complex vector "z". The real part of the vector is given by the vector "x". It is assumed that both "x" and "y" contain real numbers and have the same dimension.