SOLUTION: The expression: 2+i/3+i is equivalent to? a)6+5i/8 b)6+i/8 c)7-5i/10 d)7+i/10

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The expression: 2+i/3+i is equivalent to? a)6+5i/8 b)6+i/8 c)7-5i/10 d)7+i/10       Log On


   

Question 65864: The expression: 2+i/3+i is equivalent to?
a)6+5i/8
b)6+i/8
c)7-5i/10
d)7+i/10
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
The expression: 2+i/3+i is equivalent to?
First multiply the numerator and denominator by 3-i, the conjugate of 3+i. Now we are multiplying by(3-i)/(3-i) which equals 1
((2+i)(3-i))/((3+i)(3-i)) and this equals:
(6+3i-2i-i^2)/(9+3i-3i-i^2) and this equals:
(7+i)/10 which is d)
Note: -i^2=-(sqrt(-1))^2=-(-1)=+1
Hope this helps---ptaylor