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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: Â Â  A = 1 Â Â  B = -2 Â Â  C = 3 The 'discriminant' = B² - 4AC = -8 Roots: Â Â  D = [ -B + sqrt( B² - 4AC) ] / (2A) Â Â Â Â  = 1 + 1.414213562i and Â Â  X = [ -B - sqrt( B² - 4AC) ] / (2A) Â Â Â Â  = 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

Â 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: Â  Let A = a + bi, and B = c + di, then Â  A + B = (a + c) + (b + d)i Â Â Â Â Â Â Â  = (2 + -4) Â Â Â Â Â Â Â Â Â  + (3 + 6)i Â Â Â Â Â Â Â  = -2 + 9i |A + B| = 9.21954, arg(A+B) = 102.529° Complex Difference: Â  Let A = a + bi, and B = c + di, then Â  A - B = (a - c) + (b - d)i Â Â Â Â Â Â Â  = (2 - -4) Â Â Â Â Â Â Â Â Â  + (3 - 6)i Â Â Â Â Â Â Â  = 6 + -3i |A - B| = 6.7082, arg(A-B) = -26.5651° Complex Product: Â  Let A = a + bi, and B = c + di, then Â  A × B = (ac - bd) + (ad + bc)i Â Â Â Â Â Â Â  = (2 × -4 - 3 × 6) Â Â Â Â Â Â Â Â Â  + (2 × 6 + 3 × -4)i Â Â Â Â Â Â Â  = -26 + 0i |A × B| = 26, arg(A × B) = 180° Complex Division: Â  Let A = a + bi, and B = c + di, so |B|² = c² + d² Â Â Â Â Â Â Â  = -4² + 6² Â Â Â Â Â Â Â  = 52 Â  A ÷ B = [(ac + bd)/|B|²] + [(bc - ad)/|B|²]i Â Â Â Â Â Â Â  = [ (2 × -4 Â Â Â Â Â Â Â Â Â  + 3 × 6)/52 ] Â Â Â Â Â Â Â Â Â Â  + [ (3 × -4 Â Â Â Â Â Â Â Â Â Â Â  - 2 × 6)/52 ]i Â Â Â Â Â Â Â  = 0.192308 + -0.461538i |A ÷ B| = 0.5, arg(A ÷ B) = -67.3801°
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