Complex Numbers Flashcards
Form of a Complex Number
z=a+bi
If the discriminant is less than zero…
The equation has two distinct roots
If the discriminant equals zero…
The equation has one repeated root
If the discriminant is greater than zero…
The equation has no real roots
Complex roots come in…
Conjugate pairs
i² =
-1
Modulus Argument Form:
z=r(cosθ+isinθ)
On an argand diagram, the modulus is:
The length of the line from the origin
On an argand diagram, the argument is:
The angle the line makes with the positive x-axis
|z1z2|=
|z1||z2|
arg(z1z2)=
arg(z1)+arg(z2)
|z1/z2|=
|z1|/|z2|
arg(z1/z2)=
arg(z1)-arg(z2)
For two complex numbers, |z2-z1| represents:
The distance between z1 and z2
|z-z1|=r is the loci of:
A circle
|z-z1|=|z-z2| is the loci of:
Perpendicular bisector of z1 and z2