
How to add, subtract, multiply and divide complex numbers.
Theory:This topic shows you how to add, subtract, multiply and divide complex numbers. 1 Adding complex numbersIf 'A' and 'B' are two complex numbers, so that:
Then we can sum A and B like this:
For example, if A = 1 + 2i, and B = 3  4i, then: A + B = (1 + 3) + (2  4)i = 4  2i 2 Subtracting complex numbersIf 'A' and 'B' are two complex numbers, so that:
Then we can subtract B from A like this:
For example, if A = 1 + 2i, and B = 3  4i, then: A  B = (1  3) + (2  4)i = 2 + 6i 3 Multiplying complex numbersIf 'A' and 'B' are two complex numbers, so that:
Then we can multiply A and B like this:
For example, if A = 1 + 2i, and B = 3  4i, then: A × B = (1×3  2×(4)) + (1×(4) + 2×3)i = 11 + 2i 4 Dividing complex numbersIf 'A' and 'B' are two complex numbers, so that:
Then we can divide A by B like this: For example, if A = 1 + 2i, and B = 3  4i, then: It should be noted that the denominator terms: ( c^{2} + d^{2} ), are the square of the magnitude of complex number 'B'. ( c^{2} + d^{2} ) = B², which leads to the more compact version of the division formula:
The 'Method' section below shows you how Maths Helper Plus can display all of the working steps for adding, subtracting, multiplying or dividing complex numbers.
Method:In the following steps, we will use the examples from the 'Theory' section above. To solve your own complex number problems, insert your own numbers. Step 1 Start with an empty Maths Helper Plus documentIf you have just launched the software then you already have an empty document, otherwise hold down ‘Ctrl’ while you briefly press the ‘N’ key. Step 2 Create a complex calculator1. Press the F3 key to activate the 'input box' for typing (see below): 2. Type: com into the input box:
3. Press Enter to complete the entry
The 'options' box for the complex calculator will display immediately. Click the 'Complex Calculations' tab (see below) at the top of the options box to display the calculation options:
Click to select the operations that you want to see working steps for.
Step 3 Enter the complex numbers A and BClick the 'Complex Editor' tab at the top of the options box. This displays the 'Complex Editor' tab where you enter the complex numbers A and B to create the working steps. See below:
Click on the 'A' edit box and type complex number A like this:
( So, to enter A = 1 + 2i, type: 1,2 )
The edit box displays in yellow to show that the values have been changed.
Similarly, click on the 'B' edit box and type complex number B. ( So, to enter B = 3  4i, type: 3,4 )
Now, click the 'Apply' button at the bottom of the edit box. The text view will display the complex number calculations.
IMPORTANT: Each time you change either 'A' or 'B', remember to click the 'Apply' button to update the calculations.
The text view displays the results. To see the results, you will probably need to close the complex calculator options box by clicking the OK button.
Here are the results displayed by Maths Helper Plus for the 'A' and 'B' values entered above:
How to make changes to your complex settingsTo display the complex calculator options box at any time, double click on the text view to the left of the results display, OR if there are no results displayed, to the left of the words 'Complex Calculator'.
