SOLUTION: explain the process of multiplying or dividing of complex numbers

Question 1064080: explain the process of multiplying or dividing of complex numbers
Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.
See the lessons
    - Complex numbers and arithmetic operations on them
    - Complex plane
    - Addition and subtraction of complex numbers in complex plane
    - Multiplication and division of complex numbers in complex plane
    - Raising a complex number to an integer power

    - Solved problems on taking roots of complex numbers
    - Solved problems on arithmetic operations on complex numbers
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Complex numbers".

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
NOTE: a,b,c,d are real values.
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Multiplying is straightforward. You just use the distributive property (aka FOIL) of binomials:

Dividing is a bit more work. One first multiplies the top and bottom by the complex conjugate of the denominator to get a denominator that is a real number:

Of course, when you have numbers for a,b,c,and d, you can carry out the arithmetic until you end up with a complex number A+Bi where A and B are real numbers.
I encourage you to practice using problems you might find in your text or problems you find online. The process is not difficult but with practice it becomes even easier.

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