Step 1: Find the add of the real parts.
$$ 2+\left(-2\right) = 0 $$Step 2: Find the add of the imaginary parts.
$$ 3i+1i = 4 i$$Putting all together we have:
$$ \begin{aligned} z_1 + z_2 & = \left( 2+3i \right) + \left( -2+i \right) = \\ & = \left( 2+\left(-2\right) \right) + \left( 3i+1i \right) = \\ & = 4i \end{aligned} $$