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
5.3k views
in Complex Numbers by (49.4k points)
closed by

If z = x + iy is a complex number such that |z - 4i|/|z + 4i|. show that the locus of z is real axis.

1 Answer

+1 vote
by (48.7k points)
selected by
 
Best answer

|z - 4i|/|z + 4i|

⇒ |z – 4i| = |z + 4i| 

Let z = x + iy 

⇒ |x + iy – 4i| = |x + iy + 4i| 

⇒ |x + i(y – 4)| = |x +(y + 4)|

Squaring on both sides, we get x2 + y2 – 8y + 16 

= x2 + y2 + 16 + 8y 

⇒ -16y = 0 

⇒ y = 0 in two equation of real axis.

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.

...