Find the real numbers $x$ and $y$ if $(x-iy)(3+5i)$ is the conjugate of $-6-24i$.

If $\alpha_1, \alpha_2, \alpha_3$ respectively denote the moduli of the complex numbers $-i, \frac{1}{3}(1+i)$ and $-1+i$,then their increasing order is

If $z_1, z_2$ are two complex numbers satisfying $\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1$ and $\left|z_1\right| \neq 3$,then $\left|z_2\right|$ is equal to

If $(a+ib)(c+id)(e+if)(g+ih)=A+iB,$ then show that: $(a^{2}+b^{2})(c^{2}+d^{2})(e^{2}+f^{2})(g^{2}+h^{2})=A^{2}+B^{2}$

If $z$ is a complex number,then which of the following is not true?