# Do “complex percentages” exist?

Well, the origin of this question is a little bit strange. I dreamed - with a book called "Percentages and complex numbers. When I woke up, I thought: "Is this real?" So I started thinking:

1% of 100 = 1
3% of 100 = 3


And more:

i% of 100 = i?


That's my question. Is it right - does it even make any sense? Calculating a percentage is, basically, to multiply a fraction (denominator = 100) to a number. If it's right, we can, for example, calculate

8 + 4i% of 2 - i.


So, what you can tell me? Is it real or just a dream - have you ever seen this? And more: does it respect the definition of percentage?

Thank you.

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"$x$ per cent" literally means $x$ out of every hundred. That's why to compute x% you multiply by $\frac{x}{100}$: multiplying by $\frac{1}{100}$ tells you how many "hundreds" you have, multiplying by $x$ gives you the total amount if each hundred corresponds to $x$. So you can certainly talk about "$i$%", as the result of multiplying by $\frac{i}{100}$. But the real question is: are they good for anything? –  Arturo Magidin Oct 19 '11 at 18:28
@ArturoMagidin That's exactly what I thought. I don't really see any function, but I was curious about the existence of them. –  Ian Oct 19 '11 at 18:31

I tend to interpret % as shorthand for the fraction $\frac1{100}$; $i\%$ would just be $\frac{i}{100}$, and $(8+4i)\%$ would be $\frac2{25}+\frac{i}{25}$. As to whether these things are useful...
+1 I remember being called out in high school for using shorthand notation like $3 \cdot 50\% = 1.5$, so in the next exam I actually wrote "Let $\% = 0.01$..." –  Ilmari Karonen Oct 19 '11 at 21:08
As far as I'm concerned % is just as much of a constant as $\pi$, e, $^\circ$, etc. –  Charles Oct 19 '11 at 21:32