SOLUTION: HI ! Could you tell me if my answers are correct? #1. (-7-5i)-(12-11i) would the answer be -19+6i ? #2. (4+i)(-3+4i) would the answer be -16+13i ? #3. (1+2i) over (6-8i) wou

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: HI ! Could you tell me if my answers are correct? #1. (-7-5i)-(12-11i) would the answer be -19+6i ? #2. (4+i)(-3+4i) would the answer be -16+13i ? #3. (1+2i) over (6-8i) wou      Log On


   

Question 1041241: HI ! Could you tell me if my answers are correct?
#1. (-7-5i)-(12-11i) would the answer be -19+6i ?
#2. (4+i)(-3+4i) would the answer be -16+13i ?
#3. (1+2i) over (6-8i) would the answer be 22 over 100 + 20 over 100 i
Thank you so much
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1) Correct

# 2) Correct

# 3) The answer is actually -1%2F10+%2B+expr%281%2F5%29i. See below


-----------------------------------------------------------------------------

Steps for # 3


%281%2B2i%29%2F%286-8i%29


%28%281%2B2i%29%2F%286-8i%29%29%2A%28%286%2B8i%29%2F%286%2B8i%29%29 Multiply by %286%2B8i%29%2F%286%2B8i%29 which is a fancy form of 1


%28%281%2B2i%29%286%2B8i%29%29%2F%28%286-8i%29%286%2B8i%29%29 Combine fractions


%286%2B8i%2B12i%2B16i%5E2%29%2F%286%5E2-%288i%29%5E2%29 Expand


%286%2B8i%2B12i%2B16i%5E2%29%2F%2836-64i%5E2%29 Square each term


%286%2B8i%2B12i%2B16%28-1%29%29%2F%2836-64%28-1%29%29 Use the idea that i%5E2+=+-1


%286%2B8i%2B12i-16%29%2F%2836%2B64%29


%28-10%2B20i%29%2F100


%28-10%29%2F100%2B%2820i%29%2F100 Break up the fraction


-1%2F10%2Bexpr%281%2F5%29i Reduce




So %281%2B2i%29%2F%286-8i%29 is equivalent to -1%2F10%2Bexpr%281%2F5%29i

-----------------------------------------------------------------------------
So again, the answer for problem #3 is -1%2F10+%2B+expr%281%2F5%29i