Chapter 1: Complex Numbers Flashcards

1
Q

the complex numbers form what type of structure?

A

a field under +, x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

called “modulus”

| in complex land means

A

√x^2 + y^2 for z = x + iy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

triangle in complex land

A

|z + w| ≤ |z| + |w|

(it’s no different from the reals)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

nice property of | | ?

A

|zw| = |z| |w|

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

zw implies

A

adding angle

multiplying lengths

(use polar coordinates to derive)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly