What defines a complex number?

A complex number is defined as a combination of real and imaginary numbers. A complex number can be expressed in the form ( a + bi ), where ( a ) is the real part, ( b ) is the imaginary part, and ( i ) is the imaginary unit, which is defined as the square root of -1. This definition clearly encompasses both real numbers (when the imaginary part is zero) and truly complex numbers where the imaginary part is non-zero.

The other answers do not capture the full essence of what constitutes a complex number. Specifically, associating a complex number solely with the square root of a negative number limits the definition to only one aspect of complex numbers, as it suggests a narrower scope rather than the broader category that includes both real and imaginary components. The multiplication of a real number by itself only refers to squaring, which does not encompass the characteristics of complex numbers. Lastly, identifying a complex number as merely a square root of a positive number also fails to acknowledge the necessary inclusion of imaginary numbers that characterize the complete definition of a complex number.