Question

What is the standard form

Answer 1

C. 7/4 + √3i / 4.

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.