math 2: complex numbers Flashcards
1
Q
i²
A
-1
2
Q
i³
A
-i
3
Q
i⁴
A
1
4
Q
i⁵
A
i
5
Q
this means that iᶰ =
A
iᶰ ᵐᵒᵈ ⁴, where n mod 4 is the remainder when n is divided by 4
6
Q
the standard form of a complex number is
A
a + bi, where a and b are real
7
Q
the number a is the … of the complex number
A
real part
8
Q
the b number is called the
A
imaginary part
9
Q
if b = 0, then the complex number is just a
A
real number
10
Q
if a = 0, bi is called a
A
pure imaginary number
11
Q
when the imaginary part of a complex number is a radical, write the i to the left in order to avoid
A
ambiguity about where i is under the radical
12
Q
the modulus of a complex number is the square of its
A
distance to the origin
13
Q
the pythagorean theorem tells us that this distance is
A
√a² + b²
14
Q
(a + bi)(a - bi) =
A
a² - b²i² = a² + b²
