Everyday complex root problems come down to one relationship between atan2, cos, sin, a, b and φ. This calculator turns those numbers into r, with the working shown so you can check the result rather than simply trust it.
What Is the Complex Root Calculator?
The complex root calculator works through atan2, cos, sin, a, b and φ to give you r.
It is aimed at the case where you know the method but not the arithmetic: schoolwork, a quick check on a worked example, or a figure that needs to be right first time.
How the Complex Root Works
Each step is applied in order and depends only on the values before it, which makes it possible to follow the calculation rather than take it on trust.
If you are working through the same problem by hand afterwards, compare the intermediate values. That is where a mistake usually shows itself.
Checking Your Own Working
Round sensibly as you go and keep the full precision in the calculator. Rounding too early is the most common way of getting a right method to give a wrong answer.
Where a result should be a whole number, such as a count, check it against the constraint that produced it. A fraction of a person is a sign that something upstream needs revisiting.
A Worked Example
Working through an example, with atan2 set to 10, cos set to 5, sin set to 2, the calculator returns r of 100.49876. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out r?
Enter atan2, cos, sin, a, b and φ. The calculator then works through the relationship and reports r.
What does the complex root actually calculate?
It takes atan2, cos, sin, a, b and φ and converts them into r using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter atan2?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.