47 -14i
You can work this out in the straight-forward way, or you can recognize that (6-i) is a common factor. In the latter case, you have ...
... = (6-i)(5 + 3-i)
... = (6 -i)(8 -i)
This product of binomials is found in the usual way. Each term of one factor is multiplied by each term of the other factor and the results summed. Of course, i = √-1, so i² = -1.
... = 6·8 -6i -8i +i²
... = 48 -14i -1
... =
_____
A suitable graphing calculator will work these complex number problems easily.
Answer:
She can visit the cities in 192 ways
Step-by-step explanation:
If Sally starts from city A and after going to 4 cities she returns to home,
then that can be in 4! = 24 ways. (permutation of 4 distinct objects)
If between the time she visits cities, she comes home once,
then cities can be visited in,
= 72 ways. (permutation of 4 distinct objects and choosing 1 gap among the 3 )
If between the time she visits cities, she comes home twice,
then cities can be visited in,
=72 ways. (permutation of 4 distinct objects and finding 2 gaps among the 3)
If between the time she visits cities, she comes home thrice,
then cities can be visited in,
= 24 ways. (permutation of 4 distinct objects and choosing 3 gaps among the 3)
Now, she can't come home more than thrice in between the time she visits cities (since there are 4 cities to visit only)
So, the number of ways she can visit cities = (24+ 72 + 72 + 24)
= 192