Elements of the set C denote complex numbers.
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i is the symbol for an imaginary number, a complex number with the property i2=-1. The square root of a negative number is the square root times i. For example, the square root of -9 = 3i.
No. The power 2, which denotes squared, is one of an infinite number of possible values for the index. Indices (or powers) can be negative, fractional, irrational or even complex.
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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.