# Is 0 an imaginary number?

#### HallsofIvy

Homework Helper
The 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)

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.
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 an 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 real and imaginary.

#### CRGreathouse

Homework Helper
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 real and imaginary.
Yes, I think Jon was just lending his support.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving