How do you

How do I solve this? 3i+1/2 - 1/3(1-3i)+2

Just group all of the like terms and you are done

3i+1/2 - 1/3(1-3i)+2 =

3i + 1/2 - 1/3 + i + 2 =

2 1/6 + 4i

Simplify the following:
sqrt(abs(6-3 i))

Factor 3 out of 6-3 i giving 3 (2-i):
sqrt(abs(3 (2-i)))

abs(3 (2-i)) = 3 abs(2-i):
 sqrt(3 abs(2-i) )

abs(2-i) = sqrt(Re(2-i)^2+Im(2-i)^2) = sqrt(2^2+(-1)^2):
sqrt(3 sqrt(2^2+(-1)^2))

2^2 = 4:
sqrt(3 sqrt(4+(-1)^2))

(-1)^2 = 1:
sqrt(3 sqrt(4+1))

4+1 = 5:
sqrt(3 sqrt(5))

sqrt(3 sqrt(5)) = sqrt(sqrt(5)) sqrt(3):
sqrt(sqrt(5)) sqrt(3)

Multiply exponents. sqrt(sqrt(5)) = 5^(1/4):
Answer: |  5^(1/4) sqrt(3)