The problem is to add two complex numbers: $(\frac{1}{2} + \frac{3}{4}i)$ and $(\frac{3}{2} + \frac{3}{4}i)$.

1. Problem Description

The problem is to add two complex numbers: $(\frac{1}{2} + \frac{3}{4}i)$ and $(\frac{3}{2} + \frac{3}{4}i)$.

2. Solution Steps

To add complex numbers, we add the real parts together and the imaginary parts together.

Real parts: $\frac{1}{2} + \frac{3}{2}$

Imaginary parts: $\frac{3}{4}i + \frac{3}{4}i$

Adding the real parts:

$\frac{1}{2} + \frac{3}{2} = \frac{1+3}{2} = \frac{4}{2} = 2$

Adding the imaginary parts:

$\frac{3}{4}i + \frac{3}{4}i = (\frac{3}{4} + \frac{3}{4})i = \frac{3+3}{4}i = \frac{6}{4}i = \frac{3}{2}i$

Therefore, the sum of the two complex numbers is $2 + \frac{3}{2}i$.

3. Final Answer

$2 + \frac{3}{2}i$