Chapter 2 - argand diagrams Flashcards
What does │z│ mean
Mod z means the distance from origin to the point in graph
basically pythag to get distance
What does arguement of z mean
it is the angle measured anti clockwise from the real axis
What is the principle arguement
-π<θ≤π
What does │z1z2│ mean
│z1││z2│
also same for divisionyou multiply or divide the mods
What does arg(z1z2) mean
arg(z1) + arg(z2)
what does arg (z1/z2) mean
arg z1 - arg z2
Rule for combining mods and args of two complex numebers
- if you multiply/divide complex numbers then you x/divide mods.
- if you multiply arg z. then you ADD the arguements, and if you divide arg z then you SUBTRACT arg z1-z2
what is modulus arguement form
z= r(cosθ + isinθ)
r means modulues and θ means argz
What does │z2 - z1│ mean
distance between points z1 and z2
what does │z2 - z1│ = r mean
Circle with centre (x1,y1)
because │z - (x+iy)│= r
radius r
What happens if u square │(x-x1) + (y-y1)i│ = r
(x-x1)^2 + (y-y1)^2 = r^2
What is carteisian equation of circle with centre (a,b)
(x-a)^2 + (y-b)^2 = r^2
(a,b)
like equation of a circle
what does a locus mean
a set of points that satisfy something. it can be a line or circle etc
what does │z-z1│ = │z-z2│ mean and how to get it…
distance from z to z1 is the same as distance from z to z2
therefore, it is locus of points that are equidistant from z1 and z2.
Given by perpendicular bisector of line segment
how to get max arg z
- Tangent to the top of circle from origin
- get the angles using geometry
