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  • Let z1=2-i, z2=-2+i, find (ii) Im (1/z1 conjugate z1)

Q: 12    Let  \small z_1=2-i,z_2=-2+i.   Find 

              (ii)  \small Im\left ( \frac{1}{z_1\bar{z_1}} \right )

Answers (1)

best_answer

It is given that 
z_1= 2-i
Therefore,
\bar z_1= 2+i
NOw,
z_1\bar z_1= (2-i)(2+i)= 2^2-i^2=4+1=5                                           (using \ (a-b)(a+b)= a^2-b^2)
Now,
\frac{1}{z_1\bar z_1}= \frac{1}{5}
Therefore,
Im\left ( \frac{1}{z_1\bar z_1} \right )= 0
Therefore, the answer is 0

Posted by

Gautam harsolia

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