An imaginary number system

In a number system base $n$ you have: $\overline { \dots { x }_{ 2 }{ x }_{ 1 }{ x }_{ 0 } } =\dots +{ x }_{ 2 }\cdot { n }^{ 2 }+{ x }_{ 1 }\cdot { n }^{ 1 }+{ x }_{ 0 }\cdot { n }^{ 0 }$

Therefore in base $4+i⋅2$ we have: $\begin{aligned}z={ 424 }_{ 4+i⋅2 }&=4\cdot { \left( 4+i⋅2 \right) }^{ 2 }+2\cdot { \left( 4+i⋅2 \right) }^{ 1 }+4\cdot { \left( 4+i⋅2 \right) }^{ 0 }\\&=\left[ 48+i\cdot 64 \right] +\left[ 8+i\cdot 4 \right] +\left[ 4 \right] \\ &=60+i\cdot 68\end{aligned}$

And finally: $\boxed { Re\left( z \right) +Im\left( z \right) =128 }$