For the complex number $z$, one from $z + \bar z$ and $z\,\bar z$ is
For the complex number $z$, one from $z + \bar z$ and $z\,\bar z$ is
- A
A real number
- B
A imaginary number
- C
Both are real numbers
- D
Both are imaginary numbers
Similar Questions
Find the modulus and argument of the complex numbers:
$\frac{1+i}{1-i}$
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$\frac{1+i}{1-i}$
Let $S=\left\{Z \in C: \bar{z}=i\left(z^2+\operatorname{Re}(\bar{z})\right)\right\}$. Then $\sum_{z \in S}|z|^2$ is equal to
Let $S=\left\{Z \in C: \bar{z}=i\left(z^2+\operatorname{Re}(\bar{z})\right)\right\}$. Then $\sum_{z \in S}|z|^2$ is equal to
- [JEE MAIN 2023]
If $|{z_1}|\, = \,|{z_2}|$ and $arg\,\,\left( {\frac{{{z_1}}}{{{z_2}}}} \right) = \pi $, then ${z_1} + {z_2}$ is equal to
If $|{z_1}|\, = \,|{z_2}|$ and $arg\,\,\left( {\frac{{{z_1}}}{{{z_2}}}} \right) = \pi $, then ${z_1} + {z_2}$ is equal to
If $5 + ix^3y^2$ and $x^3 + y^2 + 6i$ are conjugate complex numbers and arg $(x + iy) = \theta $ , then ${\tan ^2}\,\theta $ is equal to
If $5 + ix^3y^2$ and $x^3 + y^2 + 6i$ are conjugate complex numbers and arg $(x + iy) = \theta $ , then ${\tan ^2}\,\theta $ is equal to
The product of two complex numbers each of unit modulus is also a complex number, of
The product of two complex numbers each of unit modulus is also a complex number, of