wow thankyou very much. Much easier to use the shortcut i would say.
One thing however, when you are saying that for the imagniary part of the log is j*pi, does j stand for the integer i.e. the absolute value of the number which the log is being taken.
e.g. ln(-1) = ln(1) + 1*pi
so ln(-2) = ln(2) + 2*pi
is this right?
Hi again,
Well, no. Lower case 'j' is used to represent what is called the
"imaginary operator", and it is used to represent the imaginary part
of complex numbers like this:
a+b*j
where
a is the real part and
b is the imaginary part.
In other words, the complex number has two distinct parts unlike an 'ordinary' number like 1, 2, 3, etc.
It's like a vector with two elements.
Sometimes lower case 'i' is used instead like this:
a+b*i
however the lower case i is often used to represent current in electrical
work, so the lower case j was adopted instead.
The numerical equivalent of j is the square root of minus 1, or:
j=sqrt(-1)
If you were to write this out in the form (real, imag) as complex numbers
sometimes are, the equivalent would be:
j=(0,1)
but the algebraic form a+b*j is still:
0+j
which of course equals j because the real part a=0 and the imaginary
part b=1. Thus, a+b*j=0+1*j.
I might add that you can never simply drop the j however, as it shows
what the imaginary part is. You can find the magnitude however by
using:
mag=sqrt(real^2+imag^2)
which is also called the amplitude sometimes.
For an example, sometimes there are two solutions to a quadratic equation that are both complex.
That is, the only solutions to the equation are complex because when inserted back into the
equation they are the only solutions that lead to a true zero result.