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It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system,
x?' = A x?
Here the eigenvalues of the matrix A are complex. By using complex eigenvalues we are going to have similar problem that we had back while we were looking at second order differential equations. We need our solutions to only have real numbers in them, though as our solutions to systems are of the form,
x?1 = ?h elt
We are going to contain complex numbers come in our solution from both the eigenvector and the eigenvalue. Getting rid of the complex numbers now will be same to how we did this back in the second order differential equation case, although will include a little more work this time around. It's simple to see how to do it in an example.
Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans: S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot
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Now we have to discuss the basic operations for complex numbers. We'll begin with addition & subtraction. The simplest way to think of adding and/or subtracting complex numbers is
Divergence Test Once again, do NOT misuse this test. This test only says that a series is definite to diverge if the series terms do not go to zero in the limit. If the
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How can I solve x in a circle? For example.. m
Division of complex number Now, we gave this formula a long with the comment that it will be convenient while it came to dividing complex numbers so let's look at a couple of e
1 1 1 1 1 2 1 2 ? and 40/2=? 2/40=?
I have a maths assignment as- Use a newspaper to study and give a report on shares and dividends.
Logarithmic form and exponential form ; We'll begin with b = 0 , b ≠ 1. Then we have y= log b x is equivalent to x= b y The first one is called
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