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
89 views
in Complex Numbers by (114k points)
closed by
The given complex number \(\frac{{1 + 4{\rm{i}}}}{{1 - 2{\rm{i}}}}\) lies in which quadrant?
1. First quadrant
2. Second quadrant
3. Third quadrant
4. Fourth quadrant
5. None of these

1 Answer

0 votes
by (115k points)
selected by
 
Best answer
Correct Answer - Option 2 : Second quadrant

Concept:

​Let z = x + iy be a complex number.

Where x is real part of the complex number and y is the imaginary part.

Calculation:

Given: complex number \(\frac{{1 + 4{\rm{i}}}}{{1 - 2{\rm{i}}}}\)

\(\begin{array}{l} \frac{{1 + 4{\rm{i}}}}{{1 - 2{\rm{i}}}} = \frac{{1 + 4{\rm{i}}}}{{1 - 2{\rm{i}}}} \times \frac{{1 + 2{\rm{i}}}}{{1 + 2{\rm{i}}}}\\ = \frac{{1 + 2{\rm{i}} + 4{\rm{i}} - 8}}{{1 + 4}} = - \frac{7}{5} + \frac{{6{\rm{i}}}}{5} \end{array}\)

We can see that the real part is negative and imaginary part is positive. 

Hence the given complex number is in second quadrant.

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.

...