When you evaluate an expression that contains a complex number, the result is usually presented as a complex number. Even expressions that involve only real numbers can have a complex value. For example, if you evaluate the square root of –1, PTC Mathcad returns 1i.

When complex numbers are available, many functions and operators become multivalued. In general, when a function or operator is multivalued, PTC Mathcad returns the principal value: the value making the smallest positive angle relative to the positive real axis in the complex plane.

For example, when you evaluate (–1)1/3, PTC Mathcad returns 0.5 + 0.866i instead of –1. This is because the number 0.5 + 0.866i makes an angle of only 60 degrees from the positive real axis. The number –1, on the other hand, is 180 degrees from the positive real axis. PTC Mathcad's nth root operator, however, returns –1 in this case.

Complex results may have only a very small imaginary part, such as roots of rapidly varying equations found numerically. When the real and imaginary parts of a result have very different scale, tolerance settings control which parts of the result are displayed.