(A) Given $z_{1} = 2 - i$.Then the conjugate $\bar{z}_{1} = 2 + i$.We know that $z_{1} \bar{z}_{1} = |z_{1}|^2 = (2)^2 + (-1)^2 = 4 + 1 = 5$.Therefore

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(A) Given $z_{1} = 2 - i$.Then the conjugate $\bar{z}_{1} = 2 + i$.We know that $z_{1} \bar{z}_{1} = |z_{1}|^2 = (2)^2 + (-1)^2 = 4 + 1 = 5$.Therefore,$\frac{1}{z_{1} \bar{z}_{1}} = \frac{1}{5}$.Since $\frac{1}{5}$ is a purely real number,its imaginary part is $0$.Thus,$\operatorname{Im}\left(\frac{1}{z_{1} \bar{z}_{1}}\right) = 0$.

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers Conjugate and Modulus of complex numbers

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Let $z_{1} = 2 - i$ and $z_{2} = -2 + i$. Find $\operatorname{Im}\left(\frac{1}{z_{1} \bar{z}_{1}}\right)$.

A
$0$
B
$1/5$
C
$1/25$
D
$1$

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1 Complex Numbers and Quadratic Equations: Complex Numbers

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Conjugate and Modulus of complex numbers

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Let $z_{1} = 2 - i$ and $z_{2} = -2 + i$. Find $\operatorname{Im}\left(\frac{1}{z_{1} \bar{z}_{1}}\right)$.

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