Hi
was wondering if anyone could help out with a niggling problem.
Complex numbers as a whole is fine- but i can't figure out (or find a lot of info)- on finding out how to calculate the reciprocal of a complex number!
i.e.
1 / (a + bi)
Thanks in advance folks.
0
Complex numbers
Started by Ali89, Nov 04 2007 05:56 PM
3 replies to this topic
#1
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Posted 04 November 2007 - 05:56 PM
#2
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Posted 06 November 2007 - 09:31 PM
Just use the conjugate complex number rule, so what you end up with is:
(a-bi) / [ (a+bi) * (a-bi) ]
(a-bi) / [ (a+bi) * (a-bi) ]
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#3
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Posted 07 November 2007 - 08:42 AM
Just to give a little bit of explanation, we start with 
. If we multiply the 
by its complex conjugate, 
, then we'll just get a real number.
So if we multiply by
, we'll get a real number on the bottom. Also, we've just multiplied by 1 so our answer is the same as the original expression.
If you remember "rationalising the denominator" from Standard Grade, it's a bit like that.
. If we multiply the by its complex conjugate, , then we'll just get a real number.So if we multiply by
, we'll get a real number on the bottom. Also, we've just multiplied by 1 so our answer is the same as the original expression.If you remember "rationalising the denominator" from Standard Grade, it's a bit like that.
#4
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Posted 10 November 2007 - 01:24 PM
QUOTE(George @ Nov 7 2007, 08:42 AM) 
Just to give a little bit of explanation, we start with . If we multiply the by its complex conjugate, , then we'll just get a real number.
So if we multiply by, we'll get a real number on the bottom. Also, we've just multiplied by 1 so our answer is the same as the original expression.
If you remember "rationalising the denominator" from Standard Grade, it's a bit like that.
. If we multiply the by its complex conjugate, , then we'll just get a real number.So if we multiply by
, we'll get a real number on the bottom. Also, we've just multiplied by 1 so our answer is the same as the original expression.If you remember "rationalising the denominator" from Standard Grade, it's a bit like that.
cheers guys. Sorry, clearly had a blonde moment as this is pretty easy stuff. Also thought as well that seeing as 1 is a complex number anyway (1 + 0i) - then you could do (1+0i)/(complex number) and that would do the same thing. Slight bit more faffin' around though doing the latter.
Thanks again.
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