JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z_1\) and \(z_2\) be any two non-zero complex numbers such that \(3\left| {{z_1}} \right| = 4\left| {{z_2}} \right|\). If \(z = \frac{{3{z_1}}}{{2{z_2}}} + \frac{{2{z_2}}}{{3{z_1}}}\) then
- A Re\((z) = 0\)
- B \(\left| z \right| = \sqrt {\frac{5}{2}} \)
- C \(\left| z \right| = \frac{1}{2}\sqrt {\frac{{17}}{2}} \)
- D Im\((z) \neq 0\)
Answer & Solution
Correct Answer
(D) Im\((z) \neq 0\)
Step-by-step Solution
Detailed explanation
\(\left|\frac{3 z_{1}}{2 z_{2}}\right|=2\) Let \(\frac{3 z_{1}}{2 z_{2}}=2 \cos \theta+2(\sin \theta) i\) \(\Rightarrow \frac{2 z_{2}}{3 z_{1}}=\frac{1}{2} \cos \theta-\frac{1}{2}(\sin \theta)\) Given, \(z=\frac{2 z_{1}}{3 z_{2}}+\frac{3 z_{2}}{2 z_{1}}\)…
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