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
324 views
in Quadratic Equations by (50.7k points)
closed by

If z2 + |z|2 = 0, show that z is purely imaginary.

1 Answer

+1 vote
by (49.2k points)
selected by
 
Best answer

Let z = a + ib

⇒ |z| = √(a2 + b2)

Now, z2 + |z|2 = 0

⇒ (a + ib)2 + a2 + b2 = 0

⇒ a2 + 2abi + i2b2 + a2 + b2 = 0

⇒ a2 + 2abi - b2 + a2 + b2 = 0

⇒ 2a2 + 2abi = 0

⇒ 2a(a + ib) = 0

Either a = 0 or z = 0

Since z ≠ 0

a = 0

⇒ z is purely imaginary

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.

...