MATLAB Programming/Complex Numbers - Wikibooks, open books for an open world (2024)

FAQs

Can MATLAB work with complex numbers? ›

In MATLAB^®, i and j represent the basic imaginary unit. You can use them to create complex numbers such as 2i+5 . You can also determine the real and imaginary parts of complex numbers and compute other common values such as phase and angle.

In Matlab complex numbers can be created using x = 3 - 2i or x = complex(3, -2). The real part of a complex number is obtained by real(x) and the imaginary part by imag(x). The complex plane has a real axis (in place of the x-axis) and an imaginary axis (in place of the y-axis).

z = complex( a , b ) creates a complex output, z , from two real inputs, such that z = a + bi .

For example: x = 5 + 6i; % x is a complex number by assignment. y = complex(5,6); % y is the complex number 5 + 6i. After assignment, you cannot change the complexity of a variable.

However, one of the journal reviewrs is saying that the scripts based on Fortran and C++ language are usually running faster than any other computational languages, and according to the reference [1] shown as follows, the MATLAB is usually 9 to 11 times slower than the best C++ executable.

In most cases, to simplify a symbolic expression using Symbolic Math Toolbox™, you only need to use the simplify function. But for some large and complex expressions, you can obtain a faster and simpler result by using the expand function before applying simplify .

Generate random numbers from the distribution. rng('default') % For reproducibility r = random(pd,10000,1);

X = randn(___,"like", p ) returns an array of random numbers like p ; that is, of the same data type and complexity (real or complex) as p . You can specify either typename or "like" , but not both. X = randn( s ,___) generates numbers from random number stream s instead of the default global stream.

X = real( Z ) returns the real part of each element in array Z .

What is the pi in MATLAB? ›

The pi in matlab is not a real 'pi', but it is only a floating-point number close to 'pi'. Trigonometric functions around pi may have errors close to machine precision. Note that sin(pi) returns '1.22464679914735e-16' and it is true somehow.

Complex numbers have three primary forms: the general form, z=a+ib; the polar form, z=r(cosθ+isinθ); and the exponential form, z=rexp(iθ).

You can use i to enter complex numbers. You also can use the character j as the imaginary unit. To create a complex number without using i and j , use the complex function. z = a + b i returns a complex numerical constant, z .

You can plot a complex number as a pair of coordinates ( x , y ) on the complex plane, also known as the Argand diagram.

In MATLAB®, you use the 'Waypoints' option to define a sequence of straight line paths from the first limit of integration to the first waypoint, from the first waypoint to the second, and so forth, and finally from the last waypoint to the second limit of integration.

The C programming language, as of C99, supports complex number math with the three built-in types double _Complex, float _Complex, and long double _Complex (see _Complex). When the header <complex. h> is included, the three complex number types are also accessible as double complex, float complex, long double complex.

B = cplxpair(A) sorts the elements along different dimensions of a complex array, grouping together complex conjugate pairs. The conjugate pairs are ordered by increasing real part. Within a pair, the element with negative imaginary part comes first. The purely real values are returned following all the complex pairs.