Question

Find the quotient. Write your answer in standard form. : 3-i/3+i

A. 1-i
B. 3/5 + 4/5 i
C. 4/5 - 3/5 i
D. -1

Answer 1

The answer is C. 4/5 - 3/5 i


`(3-i)/(3+i) = ((3-i)(3-i))/((3+i)(3-i)) \\ \\ (a+b)(a-b) = a^(2) -b^(2) \\ \\ ((3-i)(3-i))/((3+i)(3-i))= ( (3-i)^(2) )/(3^(2)-i^(2) ) \\ \\ (a-b)^(2) =a^(2)-2ab+b^(2) \\ \\ ( (3-i)^(2) )/(3^(2)-i^(2) ) = (3^(2)-2*3*i+i^(2) )/(3^(2)-i^(2) ) = (9-6i+i^(2))/(9-i^(2)) \\ \\ i = √(-1) \\ i^(2)=-1 \\ \\ (9-6i+i^(2))/(9-i^(2)) = (9-6i-1)/(9+1) = (8-6i)/(10)= (8)/(10)- (6i)/(10)= (4)/(5)- (3)/(5)i`