SOLUTION: 3+5i........5-5i 4-5i ------ and ---- + ---- 9-2i........1+5i 1+5i I have been able to solve these problems in the form of a + bi but when it comes to fractions and divid

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 3+5i........5-5i 4-5i ------ and ---- + ---- 9-2i........1+5i 1+5i I have been able to solve these problems in the form of a + bi but when it comes to fractions and divid      Log On


   

Question 351316: 3+5i........5-5i 4-5i
------ and ---- + ----
9-2i........1+5i 1+5i
I have been able to solve these problems in the form of a + bi but when it comes to fractions and dividing I am lost. Please help! Thank you so much!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
3+5i........5-5i 4-5i
------ and ---- + ----
9-2i........1+5i 1+5i
:
%283%2B5i%29%2F%289-2i%29
Multiply by the conjugate of the denominator over itself (same as mult by 1)
%283%2B5i%29%2F%289-2i%29 * %289%2B2i%29%2F%289%2B2i%29 = %2827%2B6i%2B45i%2B10i%5E2%29%2F%2881-4i%5E2%29 = %2827%2B51i%2B10%28-1%29%29%2F%2881-4%28-1%29%29 = %2827%2B51i-10%29%2F%2881%2B4%29 = %2817%2B51i%29%2F85
which is
17%2F85+%2851i%29%2F85
reduce the fractions
1%2F5 + %283i%29%2F5 = %281%2B3i%29%2F5
:
:
%28%285-5i%29%29%2F%28%281%2B5i%29%29 + %28%284-5i%29%29%2F%28%281%2B5i%29%29
these have the same denominator so we can
%28%285%2B4-5i-5i%29%29%2F%28%281%2B5i%29%29 = %28%289-10i%29%29%2F%28%281%2B5i%29%29
Multiply by the conjugate of the denominator
%28%289-10i%29%29%2F%28%281%2B5i%29%29 * %28%281-5i%29%29%2F%28%281-5i%29%29 = %28%289-45i-10i%2B50i%5E2%29%29%2F%28%281-25i%5E2%29%29 = %28%289-55i%2B50%28-1%29%29%29%2F%28%281-25%28-1%29%29%29 = %28%289-55i-50%29%29%2F%28%281%2B25%29%29 = %28-41-55i%29%2F26