SOLUTION: 7+3i ____ 3+9i how do you write this expression as a complex number in standard form?

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Question 256124: 7+3i
____
3+9i
how do you write this expression as a complex number in standard form?
Found 2 solutions by solver91311, EMStelley:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Multiply by the conjugate of the denominator divided by itself. If is a complex number, then is its conjugate.



The denominator is now the difference of two squares. Remember that .




John

Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
%287%2B3i%29%2F%283%2B9i%29
The first step in writing this expression in standard form is to multiply both the numerator and denominator by the complex conjugate of the denominator. Remember that the complex conjugate of a+bi is a-bi. So here, we want to multiply the numerator and denominator by 3-9i.
%28%287%2B3i%29%2F%283%2B9i%29%29%28%283-9i%29%2F%283-9i%29%29
This gives:
%2821-63i%2B9i-27i%5E2%29%2F%289-27i%2B27i-81i%5E2%29
Now we combine like terms, remembering that i^2 = -1.
%2821-54i%2B27%29%2F%289%2B81%29
%2848-54i%29%2F%2890%29
48%2F90+-+%2854%2F90%29i
8%2F15+-+%283%2F5%29i