# Complex Arithmetic

Robert P. Munafo, 2010 Sep 11.

All of the standard arithmetic operations can be performed with complex numbers, and there are a few new operations (notably logarithm and square root of negative numbers) that can be done with complex numbers that cannot be done with ordinary real numbers.

These examples define two complex numbers x and y as:

x = a + b i

y = c + d i

Addition and subtraction are very simple:

x+y = a+c + (b+d)i

x-y = a-c + (b-d)i

Multiplication is fairly simple too:

xy = ac - bd + (ad + bc)i

Division is a little more elaborate. Provided that c^{2}+d^{2}>0,
the quotient is:

x/y = (ac+bd)/(c^{2}+d^{2}) + (bc-ad)/(c^{2}+d^{2}) i

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2022. Mu-ency index

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2010 Sep 11. s.27