0 votes
23 views
in Complex Numbers by (33.2k points)
closed by

Find the square root of the following complex number:

2(1 – √3 i)

1 Answer

+1 vote
by (33.3k points)
selected by
 
Best answer

Let \(\sqrt{2(1-\sqrt3i)}\) = a + bi, where a, b ∈ R.

Squaring on both sides, we get

2(1 – √3 i) = a2 + b2 i2 + 2abi

2 – 2√3 i = (a2 – b2 ) + 2abi ….[∵ i2 = -1]

Equating real and imaginary parts, we get

a2 – b2 = 2 and 2ab = -2√3

a2 - b2 = 2 and b = \(-\frac{\sqrt3}a\)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...