I don't think there is such a thing. There is a "Golgi complex", also known as the "Golgi apparatus", but it is not related to numbers.
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It is a concatenation of two quite unrelated things. A Golgi complex is an organelle in most eukaryotic cells. Complex numbers are mathematical entities.
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The absolute value of a complex number is the magnitude of the number, which is found from sqrt(a² + b²) for the complex number a + bi
No. A complex number is a number that has both a real part and an imaginary part. Technically, a pure imaginary number ... which has no real part ... is not a complex number.
A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.
Yes. They are called surds. They are also complex.