# Are uncomputable numbers a subset of real numbers?

I know that Chaitin's constant is an uncomputable real number, but I'm curious as to if there are any proven examples of non-real uncomputable numbers? Could uncomputable numbers be complex?

The Wikipedia page on types of numbers says that computable numbers are real numbers. An answer on Quora says that computable numbers are complex numbers. Given that neither of these are really necessarily cited, I'm curious if there exists any mathematical definition of the computable numbers and whether that helps define the uncomputable numbers?

Thanks so much!

• Since you cite Wikipedia: "A complex number is called computable if its real and imaginary parts are computable." – Clement C. Apr 25 '18 at 4:08
• "Mathematical proof for the definition of the computable numbers"??? Definitions do not require proofs. If you want a non-real uncomputable number just multiply Chaitin's constant by $i$. – Conifold Apr 25 '18 at 4:11
• @Conifold oh... wow I'm an idiot. Didn't even consider that. Thanks! – user3684314 Apr 25 '18 at 5:30