(C) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Then the conjugate is $\bar z = x - iy$.First,$z + \bar z = (x + iy) + (x - iy) = 2x$,which is a real

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(C) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Then the conjugate is $\bar z = x - iy$.First,$z + \bar z = (x + iy) + (x - iy) = 2x$,which is a real number.Second,$z\,\bar z = (x + iy)(x - iy) = x^2 - (iy)^2 = x^2 + y^2$,which is also a real number.Therefore,both $z + \bar z$ and $z\,\bar z$ are real numbers.

Class 11 Mathematics 4-1.Complex numbers Conjugate and Modulus of complex numbers

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For the complex number $z$,which of the following is true for $z + \bar z$ and $z\,\bar z$?

A
$A$ real number
B
An imaginary number
C
Both are real numbers
D
Both are imaginary numbers

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4-1.Complex numbers

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Conjugate and Modulus of complex numbers

Let $z = a - \frac{i}{2}$,where $a \in R$. Then $|i + z|^2 - |i - z|^2$ is equal to

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For any complex number $z$,$\bar{z} = \frac{1}{z}$ if and only if

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Let complex number $z$ be such that $|z - \frac{6}{z}| = 5$,then the maximum value of $|z|$ will be -

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For the complex number $z$,which of the following is true for $z + \bar z$ and $z\,\bar z$?

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