Notation For Complex Numbers

Question

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

Answer 1

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.

Answer 2

$a + bi$, 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.

Answer 3

As far as I've seen, $z = a + ib$ is the most common with $(a, b)$ being used sometimes and $(a, 0) = a$.