Well, WitCH 1 is still not satisfactorily resolved, and Tweel’s puzzle is also still out there. But, we may as well get another ball rolling.

The second in our *What is this Crap Here* series comes from Cambridge’s textbook Specialist Mathematics VCE Units 3 & 4 (2018). Enjoy, and please get to pondering, and posting.

I will admit to using this book but never having seen this glaring issue!

Defining i=sqrt(-1) is quite different to defining i such that i^2=-1.

The +,- just adds to the sense that the author is confused. I’m hesitant to blame the author completely though as this may have been something insisted upon by the publisher or possibly even a reviewer… (or, even possibly taken from a VCAA curriculum document directly)

Thanks, Number 8. Yes, falsely declaring i = √(-1) is where the rot begins, though not where it ends.

Like sqrt(2) as a decimal in WitCH 1, it never really ends…

Don’t you refer to a and b as the real part and imaginary parts of a complex number? Not real and imaginary numbers. So bi would still be a complex number but the real part being 0 and not written.

On a side note, could you say it as no real part if a=0? I guess on the complex plane it 0 has a position and maybe you cannot say it has no real part. However, I do remember using that phrase at uni. So I’m not sure.

Hi Potii. Both are acceptable. So, for the complex number 3 + 4i, 3 is the real part and 4 is the imaginary part, but it’s still ok to say 4i is an imaginary number. In fact that expression jars with me; i’m used to “imaginary” as being a synonym for complex, and I would refer to 4i as purely imaginary in that context. But the textbook’s usage appears to be common. I don’t quite understand your second point, though note that the number 0 is both real and imaginary.

You answered my second part with 4i being said to be purely imaginary. That’s just what I was wondering, that you can say there is no real part if only there is only 4i or -13i.