If $b$ is a real number satisfying $b ^ { 4 } + \frac { 1 } { b ^ { 4 } } = 6$, find the value of $\left( b + \frac { i } { b } \right) ^ { 16 }$ where $i = \sqrt { - 1 }$.
If $b$ is a real number satisfying $b ^ { 4 } + \frac { 1 } { b ^ { 4 } } = 6$, find the value of $\left( b + \frac { i } { b } \right) ^ { 16 }$ where $i = \sqrt { - 1 }$.