okay just 2 quick ones
differentiate w = 6t^(-3/2) - 4t^(3/2)
and given that z = 1 + j and w = 2-3j find
w/z
these are the last 2 questions im stuck with and any help would be wicked cheers!.
Owwwwch!
The star means to take the complex conjugate of the variable. So since $\displaystyle z = 1 + j$, $\displaystyle z^* = 1 - j$.
Here it is in its full glory:
$\displaystyle \frac{w}{z} = \frac{2 - 3j}{1 + j}$
The problem with leaving the expression like this is that there is a radical in the denominator, $\displaystyle j = \sqrt{-1}$, which is typically removed. So if you multiply the denominator by the conjugate of the denominator (in this case rechristened as the "complex conjugate") we get:
$\displaystyle \frac{w}{z} = \frac{2 - 3j}{1 + j}$
$\displaystyle = \frac{2 - 3j}{1 + j} \cdot \frac{1 - j}{1 - j} = \frac{(2 - 3j)(1 - j)}{1^2 - j^2}$
$\displaystyle = \frac{2 - 2j - 3j + 3j^2}{1 - (-1)} = \frac{2 - 5j + 3(-1)}{1 + 1}$
$\displaystyle = \frac{-1 - 5j}{2}$
-Dan
1. European mathematicians use i exclusively for the imaginary unit. Engineers
of the electrical/electronic persuasion use j for the imaginary unit to avoid
confusion with the use of i for current (I had to go through the last paper I
sent for publication changing all the i's to j's as it was going to a
nominally electronic engineering journal, though as most of the stuff
published in it is related to DSP I think they are living in the past).
2. Often * is used to denote complex conjugate plain in ASCII maths.
RonL