1+i+1/3+корень3/3i

To simplify the expression \(1 + i + \frac{1}{3} + \frac{\sqrt{3}}{3} i\), we can first combine the real and imaginary parts separately.

1. Identify the real parts: \[ 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \]

2. Identify the imaginary parts: \[ i + \frac{\sqrt{3}}{3} i = \left(1 + \frac{\sqrt{3}}{3}\right)i \]

Now we can express the full simplified form as: \[ \frac{4}{3} + \left(1 + \frac{\sqrt{3}}{3}\right)i \]

Thus, the simplified expression is: \[ \frac{4}{3} + \left(1 + \frac{\sqrt{3}}{3}\right)i \]