Answer:
1) the types of number are the negative integers (e.g √-1 √-3 √-5 are not defined)
2) the answer is No, proof: 2x√-1 is not defined because √-1 doesn't exist
3) the answer is No, proof: √-1 - 3 is not defined because √-1 doesn't exist
4) the answer is Yes, proof: (√-1 )²= -1 this is a real number
5) the answer is No, proof: (√-1 )^3= (√-1 )²(√-1 )= - 1(√-1 ), and - 1(√-1 ) is not defined because √-1 doesn't exist
6) the result would be defined with the following cases:
√-1+n, n>1
√-1xn, n<0
√-1/n, n<0
7) the result would not be defined with the following cases:
√-1+n, n<0
√-1xn, n>0
√-1/n, n>0
8) to square 3 + √-1, I use the method of complex number
i²= -1, it implies i= √-1
so 3+√-1=3+i, and then (3+√-1)²=(3+i)²= 9 -1+6i= 8-i= 8-√-1
9) it is used for finding complex roots of a number
Explanation: