SOLUTION: The sum of two complex number is 4 and their product is 13. What are the two complex numbers? (a+bi)(c+di) = 13

Question 913204: The sum of two complex number is 4 and their product is 13. What are the two complex numbers?
(a+bi)(c+di) = 13
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!

and

and

Substituting for b into these last two equations

and

and summarizing the THREE equations which use just variables a,c,d is

The last equation in the summary of the three-equation system equivalently gives

Looking at the first equation of that system and the last equation and assuming , then

with the assumption about d allows to have the system:

Find through adding first of those to the last of those,

and then

Return to the two equation which came from the product 13.
-

----coming back to this after other steps...
-
, also from the product 13 situation
, because we know a and c

-
Again

----- or negative 3 as well.
-
Because we found

The variables a, b, c, and d, have now been solved for.
ANSWER: The two complex numbers are 2-3i and 2+3i.
----which we can soon use in substitution.

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