Complex number

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yenyen

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Given that 1/z = 1/2 + 1/(iw) + 1/(i+1)w
Express the real and imaginary parts of z in term of w.


PLEASE HELP ME PLEASE.!
 
yenyen said:
Given that 1/z = 1/2 + 1/(iw) + 1/(i+1)w
Express the real and imaginary parts of z in term of w.


PLEASE HELP ME PLEASE.!
Click to expand...

PLEASE do not post the same question more than once
 
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yenyen said:
Given that 1/z = 1/2 + 1/(iw) + 1/(i+1)w Express the real and imaginary parts of z in term of w. PLEASE HELP ME PLEASE.!
Click to expand...
I believe what I am seeing is (1) \(\displaystyle \frac{1}{z}=\frac{1}{2} + \frac{1}{i w} + \frac{1}{(i+1) w}\)
or possibly
(2) \(\displaystyle \frac{1}{z}=\frac{1}{2} + \frac{1}{i w} + \frac{1}{i+1} w\) Which is it, (1) or (2) or maybe neither?

In either case, I find it useful to clear denominators in cases like this so, assuming (1) is the right form, multiply through by 2 z w i (i+1) to get
\(\displaystyle 2 i (i+1) w = i (i+1) z w + 2 (i+1) z + 2 i z\)
Now collect terms and simplify.

There are other ways of going about getting the same answer, for example you could first write
\(\displaystyle \frac{1}{i} = \frac{1}{i} * \frac{-i}{-i} = \frac{-i}{i * (-i)}=\frac{-i}{1}=-i\)
and
\(\displaystyle \frac{1}{i+1} = \frac{1}{1+i} = \frac{1}{1+i} * \frac{1-i}{1-i} = \frac{1-i}{(1+i) * (1-i)}=\frac{1-i}{2}\) Then multiply through by 2 z w.

Of course you are not quite done but you can use the same sort of thing, multiplying numerator and denominator by the complex conjugate, to clear the complex number in the resulting denominator.

EDIT: Hopefully all dumb mistakes are corrected but I would check.
 
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