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(What does "Endorsed by" mean?)The number i and j. This double definition comes from the preference of mathematicians for using i and j are variables, and their contents may be changed. If you type j = 5, then this is the value for j and j no longer contains j = sqrt(-1) to restore the original value. Note the way a complex variable is displayed. If you type i, you should get the answer
i =
0+1.0000i.The same value will be displayed for j. Try it. Using j, you can now
enter complex variables. For example, enter z1 = 1+2*j and z2 = 2+1.5*j.
As j is a variable, you have to use the multiplication sign *. Otherwise, you
will get an error message. MATLAB does not differentiate (except in storage)
between a real and a complex variable. Therefore variables may be added, subtracted, multiplied, or even divided. For example, type in x = 2, z = 4.5*j, and z/x. The real and imaginary parts of z are both divided by x.
MATLAB just treats the real variable x as a complex variable with a zero
imaginary part. A complex variable that happens to have a zero imaginary
part is treated like a real variable. Subtract 2*j from z1 and display the
result.
MATLAB contains several built-in functions to manipulate complex numbers. For example, real (z) extracts the real part of the complex number z. Type
≫ z = 2+1.5*j, real(z)to get the result
z =
2.000+1.500i
ans =
2Similarly, imag(z) extracts the imaginary part of the complex number z. The
functions abs(z) and angle(z) compute the absolute value (magnitude) of
the complex number z and its angle (in radians). For example, type
≫ z = 2+2*j;
≫ r = abs(z)
≫ theta = angle(z)
≫ z = r*exp(j*theta)The last command shows how to get back the original complex number from its magnitude and angle. This is clarified in Chapter 1: Complex Numbers.
Another useful function, conj (z), returns the complex conjugate of
the complex number z. If z = x+j*y where x and y are real, then conj (z) is
equal to x-j*y. Verify this for several complex numbers by using the function
conj (z).
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This work is licensed by Louis Scharf under a Creative Commons Attribution License (CC-BY 3.0), and is an Open Educational Resource.
Last edited by Daniel Williamson on Sep 16, 2009 12:03 pm GMT-5.
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