Verified answer

1 / (−√3−i)

= 1 (1 + 0i) / (2 (−√3/2 − i/2))

= 1 (cos 0 + i sin 0) / (2 (cos(−5π/6) + i sin(−5π/6)))

= 1/2 (cos(0−(−5π/6)) + i sin(0−(−5π/6)))

= 1/2 (cos 5π/6 + i sin 5π/6)

= 1/2 (−√3/2 + i/2)

= −√3/4 + i/4