Complex Numbers Flashcards
1
Q
Cartesian Form of complex numbers
A
z = x + iy
2
Q
Convert to modulus argument form
A
z = r(cos(theta) + i sin(theta))
where z = root(x^2 + y^2) and theta = tan^-1(y/x)
3
Q
Complex conjugates
A
Roots come in conjugate pairs, represented as z*. This = x - iy
4
Q
How to multiply complex numbers
A
Multiply mod, add arguments
5
Q
How to divide complex numbers
A
Divide mod, subtract arguments
6
Q
How to manipulate mod-arg form. cosx - isinx =
A
cos(-x) + isin(-x)
7
Q
Perpendicular bisector of z1 and z2
A
|z-z1| = |z-z2|
8
Q
Circle radius r centre z1
A
|z - z1| = r
9
Q
Half line drawn from z1, angle x
A
arg(z-z1) = x
