Complex Numbers Flashcards
1
Q
Form of a Complex Number
A
z=a+bi
2
Q
If the discriminant is less than zero…
A
The equation has two distinct roots
3
Q
If the discriminant equals zero…
A
The equation has one repeated root
4
Q
If the discriminant is greater than zero…
A
The equation has no real roots
5
Q
Complex roots come in…
A
Conjugate pairs
6
Q
i² =
A
-1
7
Q
Modulus Argument Form:
A
z=r(cosθ+isinθ)
8
Q
On an argand diagram, the modulus is:
A
The length of the line from the origin
9
Q
On an argand diagram, the argument is:
A
The angle the line makes with the positive x-axis
10
Q
|z1z2|=
A
|z1||z2|
11
Q
arg(z1z2)=
A
arg(z1)+arg(z2)
12
Q
|z1/z2|=
A
|z1|/|z2|
13
Q
arg(z1/z2)=
A
arg(z1)-arg(z2)
14
Q
For two complex numbers, |z2-z1| represents:
A
The distance between z1 and z2
15
Q
|z-z1|=r is the loci of:
A
A circle
16
Q
|z-z1|=|z-z2| is the loci of:
A
Perpendicular bisector of z1 and z2
