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
- A
Unit modulus
- B
Less than unit modulus
- C
Greater than unit modulus
- D
None of these
Similar Questions
Let $S$ be the set of all complex numbers $z$ satisfying $\left|z^2+z+1\right|=1$. Then which of the following statements is/are $TRUE$?
$(A)$ $\left|z+\frac{1}{2}\right| \leq \frac{1}{2}$ for all $z \in S$ $(B)$ $|z| \leq 2$ for all $z \in S$
$(C)$ $\left|z+\frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$ $(D)$ The set $S$ has exactly four elements
Let $S$ be the set of all complex numbers $z$ satisfying $\left|z^2+z+1\right|=1$. Then which of the following statements is/are $TRUE$?
$(A)$ $\left|z+\frac{1}{2}\right| \leq \frac{1}{2}$ for all $z \in S$ $(B)$ $|z| \leq 2$ for all $z \in S$
$(C)$ $\left|z+\frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$ $(D)$ The set $S$ has exactly four elements
- [IIT 2020]
Amplitude of $\left( {\frac{{1 - i}}{{1 + i}}} \right)$ is
Amplitude of $\left( {\frac{{1 - i}}{{1 + i}}} \right)$ is
If $z$ is a complex number such that $|z - \bar{z}| = 2$ and $|z + \bar{z}| = 4 $, then which of the following is always incorrect -
If $z$ is a complex number such that $|z - \bar{z}| = 2$ and $|z + \bar{z}| = 4 $, then which of the following is always incorrect -
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
The complex numbers $sin\ x + i\ cos\ 2x$ and $cos\ x\ -\ i\ sin\ 2x$ are conjugate to each other, for
The complex numbers $sin\ x + i\ cos\ 2x$ and $cos\ x\ -\ i\ sin\ 2x$ are conjugate to each other, for