Flashcards
Loci on an Argard Diagram
Flashcards do conjunto (12)
- 1If Z1 = A and Z2 = B , then what is AB?|Z2-Z1|
This is the same as |-Z1+Z2|
Essientially this is a vector - 2What does arg(Z2-Z1) represent?The angle between AB and the positive direction of the x-axis
- 3What does |Z|=k represent?A circle with centre (0,0) and radius k
- 4What is a locus?A path traced out by a point subjected to certain restrictions
- 5What does |Z-Z1|=k represent?A circle with centre Z1 and radius k
- 6What does |Z-Z1|≤k represent?A circle with centre Z1 and radius K including the area inside the circle (shaded)
- 7What does |Z-Z1|=|Z-Z2| represent?A straight line which is the perpendicular bisector of the line joining Z1 and Z2
(to bisect you would need to factorise Z1 and Z2 so -1 is outside the brackets, like: |Z-(3+2i)|=|Z-(-2+i)| , and now join these points and bisect). - 8What does |Z-Z1| ≤|Z-Z2| represent?A straight line which is the perpendicular bisector of the line joining Z1 and Z2 and the half plan in which Z1 lies (shade the side where Z1 is).
- 9What is a half line?Can go to infinity in 1 direction, but doesn't go at all in the other direction.
- 10What does arg(z)=alpha represent?The half line through 0 at the angle alpha to the positive direction of the x axis
- 11What does arg(Z-Z1)=alpha represent?The half line through point Z1 at angle alpha to the positive x-axis
- 12What does (alpha ≤arg(Z-Z1) ≤beta) represent?The area on or within the half lines between alpha and beta