Principal branch

Principal branches are used in the definition of many inverse trigonometric functions, such as the selection either to define that or that A more familiar principal branch function, limited to real numbers, is that of a positive real number raised to the power of 1/2.

This relation can be satisfied by any value of y equal to a square root of x (either positive or negative).

In this instance, the positive square root function is taken as the principal branch of the multi-valued relation x1/2.

One way to view a principal branch is to look specifically at the exponential function, and the logarithm, as it is defined in complex analysis.

However, the periodic nature of the trigonometric functions involved makes it clear that the logarithm is not so uniquely determined.

Any number log z defined by such criteria has the property that elog z = z.

A branch cut, usually along the negative real axis, can limit the imaginary part so it lies between −π and π.