With math for most people, the set of complex numbers can be considered to enclose all other sets of numbers.
There are, however, sets of numbers that have been created which are outside the scope of 'complex numbers'.
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No. For example the number 1+i. Pure imaginary complex numbers are of the form 0 + a*i, where a is a non-zero real number.
No. There are complex numbers and quaternions which are not real numbers.
Yes. If the number is like, for example, 3+0i, then you'll figure out that the number, though is written as a complex number, is actually a real number 'cause 0i=0 and 3+0=3 so you have both real and complex number. Every number is a complex number, no matter if it's imaginary or real or a combination of both (a+bi).
Real numbers consist of all numbers except complex numbers. Every integer is a natural number but every rational number is not a natural number as well as an integer. So, the answer to the question is integer.
The only real (or complex) number which does not have a multiplicative inverse is 0. There is nothing you can multiply by 0 to get 1.