1. (4+2i) - (6-8i):
distribute the minus sign:
= 4 + 2i - 6 + 8i
gather like terms:
= -2 + 10i
2. i18 = i times 18. You should write it as 0 + 18i to give the answer in the form asked for.
3. (1-3i) / (2+i):
here you have to multiply the top AND bottom by the "complex conjugate" of the bottom - much in the same way you simplify radical expressions to get rid of radicals in the denominator.
the complex conjugate of any complex number, a + bi, is a - bi
So you multiply the given expression by (2-i ) / (2 - i)
The numerator becomes (1 - 3i)(2 - i) which you can foil, or use the distribute law, or the "claw method" - whatever is easiest for you since these are all really the same method:
(1 - 3i)(2 - i) = 2 - 6i - i + 3i^2 = 2 - 7i +3(-1) = 2 - 7i - 3 = -1 - 7i
(remember i^2 = -1 )
The denominator becomes (2+i)(2-i) = 4 + 2i - 2i - i^2 = 4 - (-1) = 4 + 1 = 5
ANSWER: (-1 - 7i) / 5 which can be written in a + bi form as
- 1/5 - (7/5) i