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'Complex calculator' data sets can be used as general
purpose calculators. They are called 'complex' only because they are able to
perform calculations on complex numbers. Most applications of this data set have
nothing to do with complex numbers at all.Â
You type things to calculate into the 'program' tab, and the
answers appear on the text view.
By adding a few simple commands, you can perform program loops
to generate sequences, and plot graphs at the click of a button.
Applications of the complex calculator range from working out
a simple sum like '2345 + 235', to complete solutions like a loan repayment
calculator that tabulates the payment schedule and plots a graph of the reducing
principal.
 | Program options tab: |
Type things to calculate and other program instructions into
this special dialog box:
Click the 'Run' button, and the results appear on the text
view.Â
The example program shown above is supplied with Maths
Helper Plus and solves quadratic equations. To use it, you first set the 'A',
'B' and 'C' values for the quadratic using the 'Complex Editor' tab. To
calculate the roots of the quadratic, click the 'Run' button. To plot the
roots graphically, click 'Plot'.
Here is its output for A = 1, B = -2, and C = 3: (In this
case the roots are complex.)
Output
Solve the quadratic equation Ax² + Bx + C = 0
given coefficients:
  A = 1
  B = -2
  C = 3
The 'discriminant' = B² - 4AC = -8
Roots:
  D = [ -B + sqrt( B² - 4AC) ] / (2A)
    = 1 + 1.414213562i
and
  X = [ -B - sqrt( B² - 4AC) ] / (2A)
    = 1 - 1.414213562i |
Maths Helper Plus includes many other useful complex calculator
solutions, and it is easy to write your own.Â
| Complex Editor |
Five complex number variables: 'A', 'B', 'C', 'D' and 'X'
can be used in the program expressions. View and edit these five variables
here. This tab also has a 'Run' button.
| Complex Number Calculations |
 This tab has select boxes for the four basic complex
number operations, as well as a component calculator, as shown below:
Simply set variables 'A' and 'B' to the required numbers,
then select the operations you require. All working steps are shown.
The working steps below were created by selecting all
operations on the complex numbers: A = 2 + 3i and B = -4 + 6i
Complex calculations
Complex Sum:
 Let A = a + bi, and B = c + di, then
 A + B = (a + c) + (b + d)i
       = (2 + -4)
         + (3 + 6)i
       = -2 + 9i
|A + B| = 9.21954, arg(A+B) = 102.529°
Complex Difference:
 Let A = a + bi, and B = c + di, then
 A - B = (a - c) + (b - d)i
       = (2 - -4)
         + (3 - 6)i
       = 6 + -3i
|A - B| = 6.7082, arg(A-B) = -26.5651°
Complex Product:
 Let A = a + bi, and B = c + di, then
 A × B = (ac - bd) + (ad + bc)i
       = (2 × -4 - 3 × 6)
         + (2 × 6 + 3 ×
-4)i
       = -26 + 0i
|A × B| = 26, arg(A × B) = 180°
Complex Division:
 Let A = a + bi, and B = c + di,
so |B|² = c² + d²
       = -4² + 6²
       = 52
 A ÷ B = [(ac + bd)/|B|²] + [(bc - ad)/|B|²]i
       = [ (2 × -4
         + 3 × 6)/52 ]
          + [ (3 × -4
           - 2 × 6)/52 ]i
       = 0.192308 + -0.461538i
|A ÷ B| = 0.5, arg(A ÷ B) = -67.3801° |
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