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I have seen many different notations used for complex numbers. Does it make a difference which notation is used, or is any one notation more standard than another?

I see a+bi at http://www.mathsisfun.com/numbers/complex-numbers.html

I have seen $\sigma$+it on various webpages.

σ+it

Jeffrey Young
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    You can't go wrong with $a+bi$. The letters $a$ and $b$ have no special meaning so you could write other things instead depending of what you want to express. Simply note that sometimes you may see $j$ instead of $i$ in physics. My teacher once told me it was to make a disambiguation with the $i$ of "Intensity". – Traklon Oct 08 '14 at 07:35
  • physicists use $i$ for something else, which is why they ended up using $j$. – Alan Oct 08 '14 at 07:41
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    Always be careful with electricity because it can shock you. Electric current is notated by the letter I. So when complex numbers are used for measuring emf, j is used so as to not get it confused with the notation for current. – Jeffrey Young Oct 08 '14 at 07:42

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$a + bi$, or occasionally $a + ib$, is preferred nowadays. It's best to mostly use the lowercase Roman letters for arbitrary variables and functions and leave the Greek letters for special constants and special functions.

The use of $\sigma + it$ is now mainly of historical interest, as it has been attributed to Riemann and his contemporaries. The earliest usage of $\sigma + it$ I can find is the Handbuch der Lehre von der Verteilung der Primzahlen by Edmund Landau, but with a little more searching, there may be earlier uses to be found.

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    σ+it is still much in use by Riemann zeta function aficionados, though. – Did Oct 08 '14 at 16:22
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    One person on Math Overflow said that he couldn't find a single instance of $\sigma + it$ in Riemann's original paper. I have not read that paper myself, though. –  Oct 08 '14 at 16:29
  • You noted that I did not mention Riemann papers. – Did Oct 08 '14 at 16:33
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    That still leaves the question of where did the zeta aficionados get that notation from? –  Oct 08 '14 at 16:37
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    Riemann coined $s=\frac12+\mathrm it$, for $\sigma+\mathrm it$ I don't know. – Did Oct 08 '14 at 17:23
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As far as I've seen, $z = a + ib$ is the most common with $(a, b)$ being used sometimes and $(a, 0) = a$.

Bill Thomas
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A complex number is usually written as $z=a+bi$ where $a,b$ are real. There is no essential difference between the $a+bi$ and $\sigma + it$ notation you mentioned.

please delete me
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