- #1
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I was just thinking about this question, and I see 3 possible answers:
1) 0 is a purely real complex number. This seems to be the most intuitive, however the one problem is that it shows up on the imaginary numberline.
2) 0 is not real nor imaginary. I understand this one, but I have found one problem with this: the absolute value of a complex number is modeled by the equation |x+yi|=√(x2+y2), where x and y must be real, and either can be equal to 0, and therefore 0 must be real. However, 0=0i, just as 0=-0, and 0 is thought of as neither positive or negative.
3) 0 is both real and imaginary. I'm leaning towards this one, because it appears on the real and imaginary numberlines (and other degrees of imaginary numberlines), and it can satisfy the absolute value equations as 0 can be thought of as real. I am not sure about this, however, which is why I ask.
I ruled out just imaginary because it just doesn't make sense at all, but if I'm wrong tell me.
Thanks!
1) 0 is a purely real complex number. This seems to be the most intuitive, however the one problem is that it shows up on the imaginary numberline.
2) 0 is not real nor imaginary. I understand this one, but I have found one problem with this: the absolute value of a complex number is modeled by the equation |x+yi|=√(x2+y2), where x and y must be real, and either can be equal to 0, and therefore 0 must be real. However, 0=0i, just as 0=-0, and 0 is thought of as neither positive or negative.
3) 0 is both real and imaginary. I'm leaning towards this one, because it appears on the real and imaginary numberlines (and other degrees of imaginary numberlines), and it can satisfy the absolute value equations as 0 can be thought of as real. I am not sure about this, however, which is why I ask.
I ruled out just imaginary because it just doesn't make sense at all, but if I'm wrong tell me.
Thanks!