Question

If complex numbers=a+bi if and b are 0,then complex number will become zero , then is zero a complex number

Answer 1

The answer is 'both' but the justification is different than given. An imaginary number is the square root of a nonpositive real number. Since zero is nonpositive, and is its own square root, zero can be considered imaginary.

Note that this is definitional: if an imaginary number were to be defined as the square root of a negative number, zero would not be considered imaginary, as zero is not negative. However, for reasons best left as an exercise, defining imaginary numbers in a way that excludes zero begs us to define real numbers in a way that excludes zero also.

Note that this is similar to the question: is zero positive or negative? except in that case the answer is 'neither' while in the case of real and imaginary the answer is 'both'.