# 6. Complex Numbers

Complex numbers are of interest mainly to scientists. These values are formed by a pair of numbers: a real and an imaginary component. Technically, real numbers are also complex values with an imaginary component of zero. AddUp 2 displays all numbers with a 0 imaginary value as plain real numbers. True complex numbers with a non-zero imaginary part appear as a list of two values:

sqrt(-1) = (0; -1)

The result shows that the square root of -1 is the complex number with real value 0 and imaginary value -1. You can do the reverse operation with this complex result, that is restore the square value by multiplying this complex result by itself:

(0; -1) * (0; -1) = -1

You can also use complex numbers with most AddUp functions, like the power function:

pow((1;2); (3;4)) = (0.12901; 0.03392)

With unary functions, a complex argument may look like you are using two arguments instead of only one. This single complex value can be nested within parentheses if you want to emphasize that it is a single value, but there is no need to do so:

sqr (3; 4) = (-7; 24)

sqr((3; 4)) = (-7; 24)

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