#### HallsofIvy

Science Advisor

Homework Helper

- 41,639

- 837

Then you have completely misunderstood the question! You are saying that 0 is clearly a complex number. Of course it is- every real number is a complex number. The question was whether or not 0 is anThe two definition of “imaginary numbers” depend on the context.

On is a member of the complex field defined by the operations:

(a,b)+(c,d) = (a+c,b+d)

(a,b)(c,d) = (ac-bd,bc+ad)

where a,b,c, and d are reals. In this case (0,0) = 0 is clearly a member

The other is a complex number (a number in the form of a+bi) where a=0. Cleary 0 again satisfies this since 0 = 0+0i

So I would say yes.

**imaginary**

**number.**

That has already been answered: A real number is a complex number, of the form a+ bi with b= 0. An imaginary number is a complex number, of the form a+ bi, with a= 0. The number 0 is both realThat has already been answered: A real number is a complex number, of the form a+ bi with b= 0. An imaginary number is a complex number, of the form a+ bi, with a= 0. The number 0 is both real

**and**imaginary.