Answer:
1) The conjugate for is .
2) -111
3) It is because number and its conjugate have the same numbers but their second components are opposite to each other.
Step-by-step explanation:
1) A radical number of the form , , where the first component is a non-radical real number which acts as a "pivot" and the second component is the radical component, which generates a "displacement" from pivot.
The conjugate of is a real number , , which that is "pivot" plus "displacement" in the direction opposite to that of . We proceed to complement this explanation with the image attached below.
Then, the conjugate for is .
2) We proceed to performed all the need algebraic operation until result is found:
1) Given
2) Distributive property
3) Definition of subtraction/
4) Distributive, associative and commutative properties
5) Definition of multiplication//Definition of square root
6) Commutative, associative and distributive properties/
7) Definition of subtraction/Existence of additive inverse
8)
9) Modulative property/Result
3) It is because number and its conjugate have the same numbers but their second components are opposite to each other.