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BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Functions

BITSAT 2009 · Mathematics · Functions

If ( ( z _1)= (z_2)), then

If (\arg \left(\bar{z}_1\right)=\arg \left(z_2\right)), then

Options

  1. A(\mathrm{z}}_{2}= \mathrm{kz}}_{1}^{-1}(k>\mathrm{k} \gt0))
  2. B(\mathrm{z}}_{2}=k \mathrm{z}}_{1}(k>\mathrm{k} \gt0))
  3. C(\left|z_2\right|=\left|\bar{z}_$1\right|)
  4. DNone of these

Correct answer

A. (\mathrm{z}}_{2}= \mathrm{kz}}_{1}^{-1}(k>\mathrm{k} \gt0))

Step-by-step solution

$\begin{aligned}& \bar{z}_1=\frac{z_1 \bar{z}_1}{z_1}=\left|\mathrm{z}_{1}\right|^2 \mathrm{z}}_{1}^{-1} \\ & \Rightarrow \arg \left(\mathrm{z}_{1}^{-1}\right)=\arg \left(\bar{z}_1\right) \Rightarrow \arg \left(\mathrm{z}}_{2}\right) \\ & \Rightarrow \mathrm{z}_{2}= \mathrm{kz}}_{1}^{-1}(\mathrm{k} >0) \end{aligned}$)
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