A-LevelMathematicsComplex numbers9709/31 · May/June 2024 · Q76 Marks
On a single Argand diagram sketch the loci given by the equations |z-3+2i|= 2 and |w-3+2i|=|w+3-4i| where z and w are complex numbers.
- (a)On a single Argand diagram sketch the loci given by the equations |z-3+2i|= 2 and |w-3+2i|=|w+3-4i| where z and w are complex numbers.[4]
- (b)Hence find the least value of|z-w| for points on these loci. Give your answer in an exact form.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [B1] Show a circle centre (3, -2)
- [B1FT] Show a circle with radius 2 FT centre not at the origin
- [B1] Show the point representing (-3, 4) or the midpoint (0, 1)
- [B1FT] Show the perpendicular bisector of the line joining (-3, 4) and centre of the circle
- [M1] Carry out a correct method for finding the least value of |z – w|
- [A1] Obtain answer √18-2 or 3√2-2
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