The a+bi form calculator takes magnitude (r), phase, one way, cos and sin and returns imaginary part (b) and real part (a). It is built for quick answers, for checking somebody else’s arithmetic, and for the moments when a formula book is not within reach.
What Is the A+bi Form Calculator?
The a+bi form calculator works through magnitude (r), phase, one way, cos and sin to give you imaginary part (b) and real part (a).
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 A+bi Form 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 magnitude (r) set to 10, phase set to 5, one way set to 2, the calculator returns real part (a) of 2.84, and imaginary part (b) of -9.59. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out imaginary part (b)?
Enter magnitude (r), phase, one way, cos and sin. The calculator then works through the relationship and reports imaginary part (b) and real part (a).
What does the a+bi form actually calculate?
It takes magnitude (r), phase, one way, cos and sin and converts them into imaginary part (b) and real part (a) 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 magnitude (r)?
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.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.