The minimum value of $|2z - 1| + |3z - 2|$is
The minimum value of $|2z - 1| + |3z - 2|$is
- A
$0$
- B
$1/2$
- C
$1/3$
- D
$2/3$
Similar Questions
If $z = 1 - \cos \alpha + i\sin \alpha $, then $amp \ z$=
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Let $z$ be complex number satisfying $|z|^3+2 z^2+4 z-8=0$, where $\bar{z}$ denotes the complex conjugate of $z$. Let the imaginary part of $z$ be nonzero.
Match each entry in List-$I$ to the correct entries in List-$II$.
List-$I$
List-$II$
($P$) $|z|^2$ is equal to
($1$) $12$
($Q$) $|z-\bar{z}|^2$ is equal to
($2$) $4$
($R$) $|z|^2+|z+\bar{z}|^2$ is equal to
($3$) $8$
($S$) $|z+1|^2$ is equal to
($4$) $10$
($5$) $7$
The correct option is:
Let $z$ be complex number satisfying $|z|^3+2 z^2+4 z-8=0$, where $\bar{z}$ denotes the complex conjugate of $z$. Let the imaginary part of $z$ be nonzero.
Match each entry in List-$I$ to the correct entries in List-$II$.
| List-$I$ | List-$II$ |
| ($P$) $|z|^2$ is equal to | ($1$) $12$ |
| ($Q$) $|z-\bar{z}|^2$ is equal to | ($2$) $4$ |
| ($R$) $|z|^2+|z+\bar{z}|^2$ is equal to | ($3$) $8$ |
| ($S$) $|z+1|^2$ is equal to | ($4$) $10$ |
| ($5$) $7$ |
The correct option is:
- [IIT 2023]
The solutions of equation in $z$, $| z |^2 -(z + \bar{z}) + i(z - \bar{z})$ + $2$ = $0$ are $(i = \sqrt{-1})$
The solutions of equation in $z$, $| z |^2 -(z + \bar{z}) + i(z - \bar{z})$ + $2$ = $0$ are $(i = \sqrt{-1})$
Amplitude of $\left( {\frac{{1 - i}}{{1 + i}}} \right)$ is
Amplitude of $\left( {\frac{{1 - i}}{{1 + i}}} \right)$ is
If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$then arg $({z_1}) - $arg $({z_2})$ is equal to
If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$then arg $({z_1}) - $arg $({z_2})$ is equal to
- [IIT 1979]