SOLUTION: Find the quotient of the complex numbers. {{{(-5+i)/(-7+i)}}} Part 1: Write the quotient as a fraction. Part 2: What is the conjugate of the denominator of the fraction? Part 3

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the quotient of the complex numbers. {{{(-5+i)/(-7+i)}}} Part 1: Write the quotient as a fraction. Part 2: What is the conjugate of the denominator of the fraction? Part 3      Log On


   

Question 194826: Find the quotient of the complex numbers.
%28-5%2Bi%29%2F%28-7%2Bi%29
Part 1: Write the quotient as a fraction.
Part 2: What is the conjugate of the denominator of the fraction?
Part 3: MultipPly the numerator and denominator by the conjugate of the denominator in order to rationalize the fraction. Use FOIL process to multiply the numerators and then to multiply the denominators. Combine like terms when possible. Show your work.
Part 4: Factor the GCF in the numerator and reduce the final answer. Leave your answer as a fraction in lowest terms. Show your work.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%28-5%2Bi%29%2F%28-7%2Bi%29
Multiply by the conjugate; FOIL the numerator
%28-5%2Bi%29%2F%28-7%2Bi%29 * %28-7-i%29%2F%28-7-i%29 = %28%28-5%2Bi%29%28-7-i%29%29%2F%2849+-+i%5E2%29 = %2835%2B5i-7i-i%5E2%29%2F%2849+-+%28-1%29%29 = %2835-2i-%28-1%29%29%2F%2849+%2B+1%29 = %2835-2i%2B1%29%2F%2850%29 = %2836-2i%29%2F%2850%29
simplify
2%2818-i%29%2F%2850%29 = %2818-i%29%2F25