SOLUTION: Evaluate the expression 3-i/7-3i What does the real number a equal? What does the real number b equal? Please write the result in the form a+bi

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Evaluate the expression 3-i/7-3i What does the real number a equal? What does the real number b equal? Please write the result in the form a+bi      Log On


   

Question 1001233: Evaluate the expression 3-i/7-3i
What does the real number a equal?
What does the real number b equal?
Please write the result in the form a+bi
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate the expression 3-i/7-3i
------------
To rationalize it (make the denominator a real number),
multiply the NUM and the DEN by the conjugate of the DEN 7+3i.
-----
(3-i)/(7-3i) Use parentheses.
---
(3-i)*(7+3i)/((7-3i)*(7+3i))
= (21 + 2i - 3i^2)/(49-9i^2)
= (21 + 2i + 3)/(49+9)
= (24 + 2i)/58