Which of the following are correct for any two complex numbers ${z_1}$ and ${z_2}$
Which of the following are correct for any two complex numbers ${z_1}$ and ${z_2}$
- A
$|{z_1}{z_2}|\, = \,|{z_1}||{z_2}|$
- B
$arg\,\,({z_1}{z_2}) = (arg\,{z_1})(arg\,{z_2})$
- C
$|{z_1} - {z_2}|\, \geqslant \,|{z_1}| - |{z_2}|$
- D
$(a)$ and $ (c)$ both
Similar Questions
If $z=\frac{1}{2}-2 i$, is such that $|z+1|=\alpha z+\beta(1+i), i=\sqrt{-1}$ and $\alpha, \beta \in R \quad$, then $\alpha+\beta$ is equal to
If $z=\frac{1}{2}-2 i$, is such that $|z+1|=\alpha z+\beta(1+i), i=\sqrt{-1}$ and $\alpha, \beta \in R \quad$, then $\alpha+\beta$ is equal to
- [JEE MAIN 2024]
If complex number $z = x + iy$ is taken such that the amplitude of fraction $\frac{{z - 1}}{{z + 1}}$ is always $\frac{\pi }{4}$, then
If complex number $z = x + iy$ is taken such that the amplitude of fraction $\frac{{z - 1}}{{z + 1}}$ is always $\frac{\pi }{4}$, then
If $z_1$ and $z_2$ are two unimodular complex numbers that satisfy $z_1^2 + z_2^2 = 5,$ then ${\left( {{z_1} - {{\bar z}_1}} \right)^2} + {\left( {{z_2} - {{\bar z}_2}} \right)^2}$ is equal to -
If $z_1$ and $z_2$ are two unimodular complex numbers that satisfy $z_1^2 + z_2^2 = 5,$ then ${\left( {{z_1} - {{\bar z}_1}} \right)^2} + {\left( {{z_2} - {{\bar z}_2}} \right)^2}$ is equal to -
$|{z_1} + {z_2}|\, = \,|{z_1}| + |{z_2}|$ is possible if
$|{z_1} + {z_2}|\, = \,|{z_1}| + |{z_2}|$ is possible if
If complex numbers $z_1$ and $z_2$ both satisfy $z + \overline z = 2 | z -1 |$ and $arg(z_1 -z_2) = \frac{\pi}{3} ,$ then value of $Im (z_1 + z_2)$ is, where $Im (z)$ denotes imaginary part of $z$ -
If complex numbers $z_1$ and $z_2$ both satisfy $z + \overline z = 2 | z -1 |$ and $arg(z_1 -z_2) = \frac{\pi}{3} ,$ then value of $Im (z_1 + z_2)$ is, where $Im (z)$ denotes imaginary part of $z$ -