math 2: complex numbers

Question 1

i²

Answer 1

-1

Question 2

i³

Answer 2

-i

Question 3

i⁴

Answer 3

1

Question 4

i⁵

Answer 4

i

Question 5

this means that iᶰ =

Answer 5

iᶰ ᵐᵒᵈ ⁴, where n mod 4 is the remainder when n is divided by 4

Question 6

the standard form of a complex number is

Answer 6

a + bi, where a and b are real

Question 7

the number a is the … of the complex number

Answer 7

real part

Question 8

the b number is called the

Answer 8

imaginary part

Question 9

if b = 0, then the complex number is just a

Answer 9

real number

Question 10

if a = 0, bi is called a

Answer 10

pure imaginary number

Question 11

when the imaginary part of a complex number is a radical, write the i to the left in order to avoid

Answer 11

ambiguity about where i is under the radical

Question 12

the modulus of a complex number is the square of its

Answer 12

distance to the origin

Question 13

the pythagorean theorem tells us that this distance is

Answer 13

√a² + b²

Question 14

(a + bi)(a - bi) =

Answer 14

a² - b²i² = a² + b²