Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
218 views
in Complex Numbers by (44.1k points)
closed by

Find the square roots of  15 – 8i

1 Answer

+1 vote
by (44.2k points)
selected by
 
Best answer

Let \(\sqrt{15-8i}=a+bi,\) where a, b b ∈ R.

Squaring on both sides, we get

15 – 8i = a2 + b2 i2 + 2abi

15 – 8i = (a2 – b2 ) + 2abi …..[∵ i = -1]

Equating real and imaginary parts, we get

a2 – b2 = 15 and 2ab = -8

a2 – b2 = 15 and b = \(\frac{-4}a\) 

When a = 4, b = -4/4 = -1

When a = -4, b = -4/-4 = 1

\(\therefore\sqrt{15-8i}\) = ±(4 – i)

Related questions

0 votes
1 answer
0 votes
1 answer
0 votes
1 answer
+1 vote
1 answer

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.

...