Ch2 Argand Diagrams Flashcards
1
Q
what do the axes of an argand diagram represent
A
x axis = real numbers
y axis = imaginary numbers
2
Q
what is modulus z, |z|
A
z= a+bi |z|= root(a^2 +b^2)
3
Q
what is argument of z, argz
A
z= a+bi argz = angle so that
tan(angle) = b/a
4
Q
how do you calculate agr(z) depending on quadrant
A
pos a pos b argz = tan-1(b/a)
neg a pos b argz = pi - tan-1(b/a)
pos a neg b argz = -( tan-1(b/a))
neg a neg b argz = tan-1(b/a) - pi
5
Q
how do you write complex number a+bi in modulus argument form
A
|z|=r argz=#
r(cos#+sin#i)
6
Q
|z1z2| = ?
A
|z1||z2|
7
Q
arg(z1z2) = ?
A
arg(z1) + arg (z2)
8
Q
|z1/z2|= ?
A
|z1|/|z2|
9
Q
arg(z1/z2) = ?
A
arg(z1) - arg(z2)
10
Q
what is 180 degrees in radians
A
pi
