complex numbers what does this mean

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Qxi.xli
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a complex no. is represented by the point P on the argand diagram. Given that I z- 5 +7iI =5,
sketch the locus of p

Is the questions implying that P is 5,7?? shouldn't they be more explicit?
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mqb2766
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(Original post by vix.xvi)
a complex no. is represented by the point P on the argand diagram. Given that I z- 5 +7iI =5,
sketch the locus of p

Is the questions implying that P is 5,7?? shouldn't they be more explicit?
Unless there is more to the question....
No. p/P is the locus of all points satisfying the constraint.
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DFranklin
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I think the question is expecting P to be a point satisfying the equation |z - 5 + 7i| = 5, and you're supposed to sketch the set of all possible P. (Although what you've written doesn't actually say P has anything to do with z, in which case you don't really know *anything* about P!).

Note also that with |z - 5 + 7i|, the "point of interest" is 5-7i (because you should think of |z - 5 + 7i| as |z - (5-7i)|). I can't think of any interpretation of any of this where P = (5, 7) would make sense.
Last edited by DFranklin; 1 month ago
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Qxi.xli
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(Original post by mqb2766)
Unless there is more to the question....
No. p/P is the locus of all points satisfying the constraint.
there is a part b and c but its not related/doesn't hv any useful info
(Original post by DFranklin)
I think the question is expecting P to be a point satisfying the equation |z - 5 + 7i| = 5, and you're supposed to sketch the set of all possible P. (Although what you've written doesn't actually say P has anything to do with z, in which case you don't really know *anything* about P!).

Note also that with |z - 5 + 7i|, the "point of interest" is 5-7i (because you should think of |z - 5 + 7i| as |z - (5-7i)|). I can't think of any interpretation of any of this where P = (5, 7) would make sense.
ahh kk thanks so the info about P is redundant then?
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mqb2766
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(Original post by vix.xvi)
there is a part b and c but its not related/doesn't hv any useful info

ahh kk thanks so the info about P is redundant then?
Pretty much. They often talk about a point locus though.
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Qxi.xli
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(Original post by mqb2766)
Pretty much. They often talk about a point locus though.
ahh ok thanks
sorry to disturb you again, but im just looking at some more questions which have similar wording and i keep getting confused about what they mean? In the example i gave ( a complex no. is represented by the point P on the argand diagram. Given that I z- 5 +7iI =5,
sketch the locus of p), is it trying to say that z is = p? and the only reason they've specified is so that its a 'point' and not a vector type thing?
Last edited by Qxi.xli; 1 month ago
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Muttley79
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(Original post by vix.xvi)
ahh ok thanks
sorry to disturb you again, but im just looking at some more questions which have similar wording and i keep getting confused about what they mean? In the example i gave ( a complex no. is represented by the point P on the argand diagram. Given that I z- 5 +7iI =5,
sketch the locus of p), is it trying to say that z is = p? and the only reason they've specified is so that its a 'point' and not a vector type thing?
Have you tried using these PPTs https://www.drfrostmaths.com/sow.php...term=CorePure1
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Fibonacci28
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you need to sketch the locus of all values of z where |z-5+7i| = 5
Think what |z| = 5 would look like
then think of how you need to translate it to make it |z-5+7i|=5
P appears to me to be irrelevent for this bit
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mqb2766
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(Original post by vix.xvi)
ahh ok thanks
sorry to disturb you again, but im just looking at some more questions which have similar wording and i keep getting confused about what they mean? In the example i gave ( a complex no. is represented by the point P on the argand diagram. Given that I z- 5 +7iI =5,
sketch the locus of p), is it trying to say that z is = p? and the only reason they've specified is so that its a 'point' and not a vector type thing?
In effect, yes. z is an arbitrary complex variable and they want you to think about the (z=)P points on the locus which satisfy the magnitude and/or phase constraint(s).
Last edited by mqb2766; 1 month ago
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Qxi.xli
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(Original post by Muttley79)
Have you tried using these PPTs https://www.drfrostmaths.com/sow.php...term=CorePure1
ill check them out, thanks
(Original post by mqb2766)
In effect, yes. z is an arbitrary complex variable and they want you to think about the (z=)P points on the locus which satisfy the magnitude and/or phase constraint(s).
(Original post by Fibonacci28)
you need to sketch the locus of all values of z where |z-5+7i| = 5
Think what |z| = 5 would look like
then think of how you need to translate it to make it |z-5+7i|=5
P appears to me to be irrelevent for this bit
thank you!!
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