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How to draw an Argand diagram for this complex number? (FP1)
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amelienine
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#1
If the number were 5/(1-i) let's say, how would I plot that on an Argand diagram?
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ValerieKR
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#2
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#2
(Original post by amelienine)
If the number were 5/(1-i) let's say, how would I plot that on an Argand diagram?
If the number were 5/(1-i) let's say, how would I plot that on an Argand diagram?
worked example below
Spoiler:
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5/(1-i) = ((1+i)*5)/(1+i)(1-i)=(5+5i)/2= 2.5 + 2.5i
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amelienine
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#3
(Original post by ValerieKR)
Turn it into the co-ordinate complex number form by 'realising the denominator'
Turn it into the co-ordinate complex number form by 'realising the denominator'
Spoiler:
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5/(1-i) = ((1+i)*5)/(1+i)(1-i)=(5+5i)/2= 2.5 + 2.5i
I forgot about the conjugations!! Thank you!
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RDKGames
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#4
(Original post by ValerieKR)
The easiest method for that one is to turn it into the co-ordinate complex number form by 'realising the denominator'
worked example below
The easiest method for that one is to turn it into the co-ordinate complex number form by 'realising the denominator'
worked example below
Spoiler:
Show
5/(1-i) = ((1+i)*5)/(1+i)(1-i)=(5+5i)/2= 2.5 + 2.5i
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ValerieKR
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#5
(Original post by RDKGames)
That's called rationalising the complex number. When it's rational it's then under the real category, without the imaginary part.
That's called rationalising the complex number. When it's rational it's then under the real category, without the imaginary part.
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RichE
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#6
(Original post by RDKGames)
That's called rationalising the complex number, I think. When it's rational it's then under the real category, without the imaginary part.
That's called rationalising the complex number, I think. When it's rational it's then under the real category, without the imaginary part.
e + pi i
Rationalising is certainly what you're doing when dealing with surds.
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mik1a
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#7
I prefer realising the denominator.
Rationalising is too strict, you might still want something like i/sqrt(5) with a real but irrational denominator.
Rationalising is too strict, you might still want something like i/sqrt(5) with a real but irrational denominator.
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RDKGames
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#8
(Original post by RichE)
I've seen it called both. I think actually realising is a better term for complex numbers as it would not make a lot of sense to apply the term rationalising if the denominator is
e + pi i
Rationalising is certainly what you're doing when dealing with surds.
I've seen it called both. I think actually realising is a better term for complex numbers as it would not make a lot of sense to apply the term rationalising if the denominator is
e + pi i
Rationalising is certainly what you're doing when dealing with surds.
I'll just call it "Nullifying the imaginary part" from now on.
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ValerieKR
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#9
(Original post by RDKGames)
Mhm, just the word 'realising' throws me off a bit. I think we need a proper phrase for this.
I'll just call it "Nullifying the imaginary part" from now on.
Mhm, just the word 'realising' throws me off a bit. I think we need a proper phrase for this.
I'll just call it "Nullifying the imaginary part" from now on.
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Zacken
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#10
(Original post by RDKGames)
Mhm, just the word 'realising' throws me off a bit. I think we need a proper phrase for this.
I'll just call it "Nullifying the imaginary part" from now on.
Mhm, just the word 'realising' throws me off a bit. I think we need a proper phrase for this.
I'll just call it "Nullifying the imaginary part" from now on.
Nullifying makes no sense at all, you're not nullifying the imaginary part.
(Original post by ValerieKR)
'That multiply by 1 technique'
'That multiply by 1 technique'
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RDKGames
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#11
(Original post by Zacken)
Nullifying makes no sense at all, you're not nullifying the imaginary part.
Nullifying makes no sense at all, you're not nullifying the imaginary part.
so the imaginary part disappears, hence this product can be expressed as a complex number 
where the imaginary part is null.
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atsruser
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#12
(Original post by RichE)
I've seen it called both. I think actually realising is a better term for complex numbers as it would not make a lot of sense to apply the term rationalising if the denominator is
e + pi i
Rationalising is certainly what you're doing when dealing with surds.
I've seen it called both. I think actually realising is a better term for complex numbers as it would not make a lot of sense to apply the term rationalising if the denominator is
e + pi i
Rationalising is certainly what you're doing when dealing with surds.
http://www.thestudentroom.co.uk/show...45&postcount=7
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atsruser
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#13
(Original post by RDKGames)
Mhm, just the word 'realising' throws me off a bit. I think we need a proper phrase for this.
I'll just call it "Nullifying the imaginary part" from now on.
Mhm, just the word 'realising' throws me off a bit. I think we need a proper phrase for this.
I'll just call it "Nullifying the imaginary part" from now on.
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Zacken
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#14
(Original post by RDKGames)
Are you practically not? so the imaginary part disappears, hence this product can be expressed as a complex number where the imaginary part is null.
Are you practically not?
so the imaginary part disappears, hence this product can be expressed as a complex number where the imaginary part is null.
which certainly has an imaginary part. Unless you want to call it "nullifying the imaginary part of the denominator", which is a mouthful.
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RDKGames
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#15
(Original post by Zacken)
Huh? Take which certainly has an imaginary part. Unless you want to call it "nullifying the imaginary part of the denominator", which is a mouthful.
Huh? Take
which certainly has an imaginary part. Unless you want to call it "nullifying the imaginary part of the denominator", which is a mouthful.
but yeah I meant it as far as the denominator is concerned in my comment. Meh, I wouldn't say it's too much of a mouthful.
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RichE
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#16
(Original post by atsruser)
The obvious choice might be "reifying" but that's already got too many uses, so how about "decomplexifying"?
The obvious choice might be "reifying" but that's already got too many uses, so how about "decomplexifying"?
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atsruser
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#17
(Original post by RichE)
That would seem to imply real numbers aren't complex (which they are).
That would seem to imply real numbers aren't complex (which they are).
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RichE
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#18
(Original post by atsruser)
Maybe, but you could make the same objection to the term "realising", so I don't think it's any worse than that. I suspect that it's a pointless discussion anyway, as too many people are happy to misuse "rationalise" in this context.
Maybe, but you could make the same objection to the term "realising", so I don't think it's any worse than that. I suspect that it's a pointless discussion anyway, as too many people are happy to misuse "rationalise" in this context.
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atsruser
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#19
(Original post by RichE)
I don't see your point as most complex numbers aren't real. You are making real a typically complex denominator.
I don't see your point as most complex numbers aren't real. You are making real a typically complex denominator.
"That would seem to imply real numbers aren't complex (which they are)."
Anyway, I don't think the current usage will ever change, so this will be my final contribution on this particular prickly question of nomenclature.
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RichE
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#20
(Original post by atsruser)
I'm afraid I don't understand what you're saying here. Your second sentence doesn't seem to agree with what you said in your previous post:
"That would seem to imply real numbers aren't complex (which they are)."
Anyway, I don't think the current usage will ever change, so this will be my final contribution on this particular prickly question of nomenclature.
I'm afraid I don't understand what you're saying here. Your second sentence doesn't seem to agree with what you said in your previous post:
"That would seem to imply real numbers aren't complex (which they are)."
Anyway, I don't think the current usage will ever change, so this will be my final contribution on this particular prickly question of nomenclature.
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