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JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \({Z_1} \ne 0\) and \(Z_2\) be two complex numbers such that \(\frac{{{Z_2}}}{{{Z_1}}}\) is a purely imaginary number, then \(\left| {\frac{{2{Z_1} + 3{Z_2}}}{{2{Z_1} - 3{Z_2}}}} \right|\) is equal to
- A \(2\)
- B \(5\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
Let \({\text{ }}{z_1} = 1 + i{\text{ }}\) and \({z_2} = 1 - i\) \(\frac{{{z_2}}}{{{z_1}}} = \frac{{1 - i}}{{1 + i}} \) \(= \frac{{(1 - i)(1 - i)}}{{(1 + i)(1 - i)}}\, = \, - \,i\) \(\frac{{2{z_1} + 3{z_2}}}{{2{z_1} - 3{z_2}}} = \)…
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