Answer:
C. 7/4 + √3i / 4.
Step-by-step explanation:
(1 + 2√-3) / (1 + √-3)
Since √-1 = i we have:
(1 + 2√3i) / (1 + √3i)
Multiply top and bottom by the conjugate (1 - √3i):
(1 + 2√3i)( (1 - √3i) / (1 + √3i) (1 - √3i)
= 1 - √3 i + 2√3 i + 6) ( 1 + 3)
= 7 +√3i / 4
= 7/4 + √3i / 4.
