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AP EAMCET · Maths · Complex Number

The multiplicative inverse of \(\mathrm{z}\) is

  1. A \(\frac{1}{z+\bar{z}}\)
  2. B \(\frac{z}{|\bar{z}|}\)
  3. C \(\frac{\bar{z}}{|z|^2}\)
  4. D \(\frac{1}{\bar{z}}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\bar{z}}{|z|^2}\)

Step-by-step Solution

Detailed explanation

Let multiplicative inverse of \(\mathrm{z}\), be 'A' hence \(\mathrm{z} \cdot \mathrm{A}=1\) \(\Rightarrow \quad A=\frac{1}{z}=\frac{1 \cdot \bar{z}}{z \cdot \bar{z}} \quad\) (where \(\bar{z}\) is conjugate of \(z\) )…