On the complex plane, let $\bar { z }$ denote the complex conjugate of complex number $z$, and $i = \sqrt { - 1 }$. Select the correct options. (1) If $z = 2 i$, then $z ^ { 3 } = 4 \bar { i } \bar { z }$ (2) If non-zero complex number $\alpha$ satisfies $\alpha ^ { 3 } = 4 i \bar { \alpha }$, then $| \alpha | = 2$ (3) If non-zero complex number $\alpha$ satisfies $\alpha ^ { 3 } = 4 i \bar { \alpha }$ and let $\beta = i \alpha$, then $\beta ^ { 3 } = 4 i \bar { \beta }$ (4) Among all non-zero complex numbers $z$ satisfying $z ^ { 3 } = 4 i \bar { z }$, the minimum possible value of the principal argument is $\frac { \pi } { 6 }$ (5) There are exactly 3 distinct non-zero complex numbers $z$ satisfying $z ^ { 3 } = 4 i \bar { z }$
On the complex plane, let $\bar { z }$ denote the complex conjugate of complex number $z$, and $i = \sqrt { - 1 }$. Select the correct options.\\
(1) If $z = 2 i$, then $z ^ { 3 } = 4 \bar { i } \bar { z }$\\
(2) If non-zero complex number $\alpha$ satisfies $\alpha ^ { 3 } = 4 i \bar { \alpha }$, then $| \alpha | = 2$\\
(3) If non-zero complex number $\alpha$ satisfies $\alpha ^ { 3 } = 4 i \bar { \alpha }$ and let $\beta = i \alpha$, then $\beta ^ { 3 } = 4 i \bar { \beta }$\\
(4) Among all non-zero complex numbers $z$ satisfying $z ^ { 3 } = 4 i \bar { z }$, the minimum possible value of the principal argument is $\frac { \pi } { 6 }$\\
(5) There are exactly 3 distinct non-zero complex numbers $z$ satisfying $z ^ { 3 } = 4 i \bar { z }$