Answer:
(2 (3 i + 1))/5
Explanation:
Simplify the following:
(4 i)/(i + 3)
Multiply numerator and denominator of (4 i)/(i + 3) by 3 - i:
(4 i (-i + 3))/((i + 3) (-i + 3))
(3 + i) (3 - i) = 3×3 + 3 (-i) + i×3 + i (-i) = 9 - 3 i + 3 i + 1 = 10:
(4 i (-i + 3))/10
The gcd of 4 and 10 is 2, so (4 i (-i + 3))/10 = ((2×2) i (-i + 3))/(2×5) = 2/2×(2 i (-i + 3))/5 = (2 i (-i + 3))/5:
(2 i (-i + 3))/5
i (3 - i) = 1 + 3 i:
Answer: (2 (3 i + 1))/5