Number Theory

Question 1

Closure property- natural numbers are closed under what and what ?

Answer 1

Natural numbers are closed only under multiplication and addition
A X B = Natural number
A + B = Natural number

Question 2

Commutative property- natural numbers are commutative under what and what ?

Answer 2

Addition & multiplication
A + B = B + A
A x B = B x A

Question 3

Associative property- natural numbers are associative under what and what ?

Answer 3

Addition & Multiplication
a + (b+c) = (a+b) + c
a x (bxc) = (axb) x c

Question 4

Distributive property- natural numbers are distributive under what ?

Answer 4

Multiplication
a x (b+c) = (axb) + (axc)

Question 5

Natural numbers

Answer 5

N = {1,2,3,4,5…..}
“Excluding 0”

Question 6

Whole numbers

Answer 6

W = {0,1,2,3,4…..}
“All natural numbers including 0”

Question 7

Complex numbers (C) have imaginary numbers like

Answer 7

¡ = sqr(-1)
E.g 3 - 5¡

Question 8

All real and imaginary numbers are

Answer 8

Complex numbers

Question 9

How to add complex numbers

Answer 9

(a + b¡) + (c + d¡) = (a + c) + (b + d) * ¡

Question 10

Multiplying complex numbers

Answer 10

Multiply normally but ¡^2 is always -1

Question 11

Conjugate 3 - 2¡

Answer 11

3 + 2¡

Question 12

Division of complex numbers

Answer 12

Rationalize