Find the complex number z satisfying the equations $\left| {\frac{{z - 12}}{{z - 8i}}} \right| = \frac{5}{3},\left| {\frac{{z - 4}}{{z - 8}}} \right| = 1$
Find the complex number z satisfying the equations $\left| {\frac{{z - 12}}{{z - 8i}}} \right| = \frac{5}{3},\left| {\frac{{z - 4}}{{z - 8}}} \right| = 1$
- A
$6$
- B
$6 \pm 8i$
- C
$6 + 8i,\,6 + 17i$
- D
None of these
Similar Questions
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]
$arg\,(5 - \sqrt 3 i) = $
$arg\,(5 - \sqrt 3 i) = $
Find the modulus of $\frac{1+i}{1-i}-\frac{1-i}{1+i}$
Find the modulus of $\frac{1+i}{1-i}-\frac{1-i}{1+i}$
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
If $z$ and $\omega$ are two complex numbers such that $|z \omega|=1$ and $\arg (z)-\arg (\omega)=\frac{3 \pi}{2}$, then $\arg \left(\frac{1-2 \bar{z} \omega}{1+3 \bar{z} \omega}\right)$ is:
(Here arg(z) denotes the principal argument of complex number $z$ )
If $z$ and $\omega$ are two complex numbers such that $|z \omega|=1$ and $\arg (z)-\arg (\omega)=\frac{3 \pi}{2}$, then $\arg \left(\frac{1-2 \bar{z} \omega}{1+3 \bar{z} \omega}\right)$ is:
(Here arg(z) denotes the principal argument of complex number $z$ )
- [JEE MAIN 2021]