$\sqrt[4]{17 + 12\sqrt{2}} = $

If $\sqrt{a + ib} = x + iy$,then the possible value of $\sqrt{a - ib}$ is

If $a > 0$ and $z = x + iy$,then $\log_{\cos^2 \theta} |z - a| > \log_{\cos^2 \theta} |z - ai|$ for $\theta \in R$ implies:

If the real parts of $\sqrt{-5-12 i}$ and $\sqrt{5+12 i}$ are positive,the real part of $\sqrt{-8-6 i}$ is negative,and $a+i b = \frac{\sqrt{-5-12 i}+\sqrt{5+12 i}}{\sqrt{-8-6 i}}$,then $2 a+b =$

If $z = i \log (2 - \sqrt{3}),$ then $\cos z = $

If $(-7 - 24i)^{1/2} = x - iy$,then $x^2 + y^2 = $