SOLUTION: Find the product of 1+3i and it's conjugate. The answer is a a+bi where: The real number a equals________ The real number b equals________

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Question 1001113: Find the product of 1+3i and it's conjugate. The answer is a a+bi where:
The real number a equals________
The real number b equals________
Found 2 solutions by MathLover1, solver91311:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The conjugate of 1+%2B+3i is 1+-+3i
the product is:
%281+%2B+3i%29%281+-+3i%29+=+1%5E2+-+%283i%29%5E2
%281+%2B+3i%29%281+-+3i%29+=+1%5E2+-+3%5E2%28i%29%5E2...i%5E2+=++-1
You end up with 1+-+9%28-1%29
So it becomes 1+%2B9
Which equals 10+

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The product of any binomial and its conjugate is the difference of two squares. Just remember that , so that is the sum of the squares of the two real parts and is zero.

John

My calculator said it, I believe it, that settles it