Discussion
The modulus of the complex number \(\left(\frac{i}{2} - \frac{2}{i}\right)\) is equal to
Answer: E
The modulus is \(\frac{5}{2}\).
Simplify \(\frac{2}{i}\) first: multiplying top and bottom by \(i\) gives \(\frac{2i}{i^{2}} = -2i\). Then:
\[ \begin{aligned} \frac{i}{2} - \frac{2}{i} &= \frac{i}{2} + 2i \\ &= \frac{5i}{2} \\ \left|\frac{5i}{2}\right| &= \frac{5}{2} \end{aligned} \]
The number is purely imaginary, so its modulus is just the size of the coefficient of \(i\). Writing \(\frac{2}{i}\) as \(+2i\) instead of \(-2i\) gives \(\frac{i}{2} - 2i = -\frac{3i}{2}\) and the distractor \(\frac{3}{2}\).
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development