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# Argand diagrams (New Further Maths A level) watch

1. Can anyone explain to me what I need to do for these three parts and what they're actually asking me to do? I just need some guidance on what I actually need to do in order to solve them.
2. (Original post by MathsMeme)
Can anyone explain to me what I need to do for these three parts and what they're actually asking me to do? I just need some guidance on what I actually need to do in order to solve them.
It's pretty clear what you need to do, what bit are you stuck on?
3. (Original post by MathsMeme)
Can anyone explain to me what I need to do for these three parts and what they're actually asking me to do? I just need some guidance on what I actually need to do in order to solve them.
The first two are "locus" problems. The locus of an equation is the set of points which satisfy it i.e. the set of points which lie on the curve defined by it. So you need to be able to figure out which points in the complex plane the following type of eqn is true:

where a and b are fixed complex numbers and z represents any of those complex numbers (i.e. points in the plane) for which that eqn is true.

Hint: is the distance in the plane from a to z.

Similarly where r is constant says what about the z's that satisfy it?

It probably will help you to draw out the complex plane and mark two random points a and b then think about the constraints that the eqns above put on z
4. (Original post by NotNotBatman)
It's pretty clear what you need to do, what bit are you stuck on?
For A, cause it's equal to the modulus of z I'm not sure how it should look sketched out.

For B, just not sure how I'd go about finding the complex numbers that satisfy both
5. (Original post by MathsMeme)
For A, cause it's equal to the modulus of z I'm not sure how it should look sketched out.

For B, just not sure how I'd go about finding the complex numbers that satisfy both
|z-6| = |z-0|, this is one of the perpendicular bisector forms.

for part b, it's essentially the points of intersection of the two loci.
6. (Original post by NotNotBatman)
|z-6| = |z-0|, this is one of the perpendicular bisector forms.

for part b, it's essentially the points of intersection of the two loci.
Would it be the two points of intersection of the circle and the perpendicular bisector? Apologies, I haven't been taught this for some reason
7. (Original post by MathsMeme)
Would it be the two points of intersection of the circle and the perpendicular bisector? Apologies, I haven't been taught this for some reason
Yes.

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