SOLUTION: 2+3i 7-2i ---- + ---- 3-2i 8+i the answer is 54+42i ------ 65 but i don't know HOW my teacher got that. can you explain?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 2+3i 7-2i ---- + ---- 3-2i 8+i the answer is 54+42i ------ 65 but i don't know HOW my teacher got that. can you explain?       Log On


   

Question 369901: 2+3i 7-2i
---- + ----
3-2i 8+i
the answer is
54+42i
------
65

but i don't know HOW my teacher got that. can you explain?



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2+3i 7-2i
---- + ----
3-2i 8+i
-----------
Step 1, get the i's out of the denominators. Multiply NUM and DEN by the conjugate of the DEN
---------
(2+3i)*(3+2i) (7-2i)*(8-i)
------------- + -----------
(3-2i)*(3+2i) (8+i)*(8-i)
---
(6+13i-6) (56 - 23i - 2)
--------- + -----------
(9 + 4) (64 + 1)
---
13i (54 - 23i)
--- + ----------
13 65
= (54 - 23i)/65 + i
= (54 - 23i)/65 + 65i/65
= (54 + 42i)/65