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!.

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- Aug 15th 2007, 01:59 PMmxmadman_44differentiation and complex numbers
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!. - Aug 15th 2007, 02:12 PMThePerfectHacker
- Aug 15th 2007, 02:25 PMPlato
- Aug 15th 2007, 03:17 PMmxmadman_44complex number
yes its a complex number division the equation i have is wz*/|z|^2

im not sure what the star means. should i ignore this?

any help on the differentiation would be great im not sure what to do with the negative fraction powers - Aug 15th 2007, 03:30 PMtopsquark
- Aug 15th 2007, 03:36 PMtopsquark
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 - Aug 15th 2007, 03:45 PMPlato
Star? What Star?

The conjugate of z is $\displaystyle {\overline z }$.

Does that appear as z* in your browser? If so, what is the browser? - Aug 15th 2007, 03:49 PMmxmadman_44star
- Aug 15th 2007, 04:19 PMPlato
- Aug 15th 2007, 04:57 PMtopsquark
- Aug 15th 2007, 08:36 PMCaptainBlack
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