The Modulus and the Conjugate of a Complex Number

Find the modulus of conjugate of given complex number.

$z=3+2i$

Find the modulus of conjugate of given complex number.

$z=-2+3i$

Find the modulus of conjugate of given complex number.

$z=-2-3i$

Find the modulus of conjugate of given complex number.

$z=2-3i$

Find the modulus of conjugate of given complex number.

$z=2+3i$

The modulus of $e^{iz}$, if $z=x+iy$ is a complex number, where $x$ and $y$ are real numbers, is

Find the conjugate of $\frac{1}{3+4i}$.

If $z=x+iy$ and $\left|z\right|=1$, find the locus of $z$.

The modulus amplitude form of complex number $-1-i\sqrt{3}$ is

If $z$ is a complex number such that $\left|z-\frac{6}{z}\right|=5,$ then the maximum value of $\left|z\right|$ among the following option is

The locus of $z$ satisfying $\left|\frac{z-i}{z-2i}\right|=2$ is a

If $z=\cos \frac{\pi }{4}+i\sin \frac{\pi }{6},$ then

The modulus of the complex number $\frac{(1-i\sqrt{3})(\cos \theta +i\sin \theta )}{(1+i)(\cos \theta -i\sin \theta )}$ is

If $x+iy=(1+i)(2+i)(3+i),$ then $x^2+y^2$ is equal to

For any complex number $z,$ which of the following is not true?

If $|z-i|<|z+i|$, then

If $\left|z_1\right|=\left|z_2\right|$, is it necessary that $z_1=z_2$ ?

Where does z lie, if $\left|\frac{z-5i}{z+5i}\right|=1$

If $\frac{{\left(a^2+1\right)}^2}{2a-i}=x+iy$, what is the value of $k$ in $x^2+y^2=\frac{{\left(a^2+1\right)}^4}{k{a}^2+1}$ ?

If the conjugate of $\frac{2-i}{(1-2i{)}^2}$ is $\overline{z}=k+mi$, then $k+m=$