If $x + iy = \frac{3}{2 + \cos \theta + i\sin \theta}$,then ${x^2} + {y^2}$ is equal to

If $z$ is a complex number with $|z| \geq 5$,then the least value of $\left|z+\frac{2}{z}\right|$ is

If $m_1, m_2, m_3$ and $m_4$ respectively denote the moduli of the complex numbers $1+4i, 3+i, 1-i$ and $2-3i$,then the correct relation among the following is:

For real numbers $a$ and $b$,if $4a + i(3a - b) = b - 6i$ and $z = a + \frac{b}{4}i$,then $\frac{|z|}{a} = $

If $|a_k| < 1, \lambda_k \ge 0$ for $k = 1, 2, ..., n$ and $\lambda_1 + \lambda_2 + ... + \lambda_n = 1$,then the value of $|\lambda_1 a_1 + \lambda_2 a_2 + ... + \lambda_n a_n|$ is

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